{"id":6669,"date":"2023-02-07T20:44:05","date_gmt":"2023-02-07T15:14:05","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=6669"},"modified":"2023-02-10T14:59:44","modified_gmt":"2023-02-10T09:29:44","slug":"go-math-grade-8-answer-key-chapter-9-transformations-and-congruence","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/go-math-grade-8-answer-key-chapter-9-transformations-and-congruence\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence"},"content":{"rendered":"<p>There are multiple ways to learn maths. But choosing the best material is also important for the students to score good marks and also to improve their knowledge. This will be possible only with the help of our Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence. You can get the explanation for all the questions in detail in Go Math Grade 8 Chapter 9 Transformations and Congruence Answer Key here. Refer to <a href=\"https:\/\/ccssanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> for learning the problems in an easy manner.<\/p>\n<h2>Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence<\/h2>\n<p>Practice makes you perfect become a master in maths. Without proper knowledge on the subject, you cannot solve the problems in real-time. This will affect your exam. So, keeping this in our mind we have prepared the solutions briefly which will help you to understand the concept in depth. Get free access to Download Go Math Grade 8 Chapter 9 Transformations and Congruence Solution Key pdf. In this article, you will get the solutions according to the topics. Therefore, students who want to score good marks in the exam must practice with Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence.<\/p>\n<p><strong>Lesson 1: Properties of Translations<\/strong><\/p>\n<ul>\n<li><a href=\"#Properties_of_Translations_\u2013_Page_No._282\">Properties of Translations \u2013 Page No. 282<\/a><\/li>\n<li><a href=\"#Properties_of_Translations_\u2013_Page_No._283\">Properties of Translations \u2013 Page No. 283<\/a><\/li>\n<li><a href=\"#Properties_of_Translations_Lesson_Check_\u2013_Page_No._284\">Properties of Translations Lesson Check \u2013 Page No. 284<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Properties of Reflections<\/strong><\/p>\n<ul>\n<li><a href=\"#Properties_of_Reflections_\u2013_Page_No._288\">Properties of Reflections \u2013 Page No. 288<\/a><\/li>\n<li><a href=\"#Properties_of_Reflections_\u2013_Page_No._289\">Properties of Reflections \u2013 Page No. 289<\/a><\/li>\n<li><a href=\"#Properties_of_Reflections_Lesson_Check_\u2013_Page_No._290\">Properties of Reflections Lesson Check \u2013 Page No. 290<\/a><\/li>\n<li><a href=\"#Properties_of_Reflections_Lesson_Check_1_\u2013_Page_No._294\">Properties of Reflections Lesson Check 1 \u2013 Page No. 294<\/a><\/li>\n<li><a href=\"#Properties_of_Reflections_Lesson_Check_2_\u2013_Page_No._295\">Properties of Reflections Lesson Check 2 \u2013 Page No. 295<\/a><\/li>\n<li><a href=\"#Properties_of_Reflections_Lesson_Check_3_\u2013_Page_No._296\">Properties of Reflections Lesson Check 3 \u2013 Page No. 296<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Algebraic Representations of Transformations<\/strong><\/p>\n<ul>\n<li><a href=\"#Algebraic_Representations_of_Transformations_\u2013_Page_No._300\">Algebraic Representations of Transformations \u2013 Page No. 300<\/a><\/li>\n<li><a href=\"#Algebraic_Representations_of_Transformations_\u2013_Page_No._301\">Algebraic Representations of Transformations \u2013 Page No. 301<\/a><\/li>\n<li><a href=\"#Algebraic_Representations_of_Transformations_Lesson_Check_\u2013_Page_No._302\">Algebraic Representations of Transformations Lesson Check \u2013 Page No. 302<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Congruent Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Congruent_Figures_\u2013_Page_No._306\">Congruent Figures \u2013 Page No. 306<\/a><\/li>\n<li><a href=\"#Congruent_Figures_\u2013_Page_No._307\">Congruent Figures \u2013 Page No. 307<\/a><\/li>\n<li><a href=\"#Congruent_Figures_Lesson_Check_\u2013_Page_No._308\">Congruent Figures Lesson Check \u2013 Page No. 308<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#Model_Quiz_\u2013_Page_No._309\">Model Quiz \u2013 Page No. 309<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review<\/strong><\/p>\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._310\">Mixed Review \u2013 Page No. 310<\/a><\/li>\n<\/ul>\n<h3><a id=\"Properties_of_Translations_\u2013_Page_No._282\"><\/a>Guided Practice &#8211; Properties of Translations &#8211; Page No. 282<\/h3>\n<p>Question 1.<br \/>\nVocabulary A __________________is a change in the position, size, or shape of a figure.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ntransformation<\/p>\n<p>Explanation:<br \/>\nA transformation is a change in the position, size, or shape of a figure.<\/p>\n<p>Question 2.<br \/>\nVocabulary When you perform a transformation of a figure on the coordinate plane, the input of the transformation is called the ________________, and the output of the transformation is called the_________________ .<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\npre-image<br \/>\nimage<\/p>\n<p>Explanation:<br \/>\nWhen you perform a transformation of a figure on the coordinate plane, the input of the transformation is called the pre-image, and the output of the transformation is called the image.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168499\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q3.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 282 Q3\" width=\"649\" height=\"434\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q3.png 649w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q3-300x201.png 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168500\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q4.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 282 Q4\" width=\"650\" height=\"444\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q4.png 650w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-282-Q4-300x205.png 300w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><\/p>\n<p>Question 5.<br \/>\nThe figure shows trapezoid WXYZ. Graph the image of the trapezoid after a translation of 4 units up and 2 units to the left.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 1\" width=\"252\" height=\"215\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter translation:<br \/>\nW'(-4, 3)<br \/>\nX'(2, 3)<br \/>\nY'(1, 1)<br \/>\nZ'(-3, 1)<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 6.<br \/>\nWhat are the properties of translations?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n-&gt; a translation is a geometric transformation that moves every point of a figure or space by the same amount in a given direction.<br \/>\n-&gt; So the figures are identical and are congruent.<\/p>\n<h3><a id=\"Properties_of_Translations_\u2013_Page_No._283\"><\/a>9.1 Independent Practice &#8211; Properties of Translations &#8211; Page No. 283<\/h3>\n<p>Question 7.<br \/>\nThe figure shows triangle DEF.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 2\" width=\"301\" height=\"255\" \/><br \/>\na. Graph the image of the triangle after the translation that maps point D to point D &#8216;.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2 left, and 4 down<\/p>\n<p>Question 7.<br \/>\nb. How would you describe the translation?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIt has the same size, shape. and orientation, but a different location<\/p>\n<p>Question 7.<br \/>\nc. How does the image of triangle DEF compare with the preimage?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ncongruent<\/p>\n<p>Question 8.<br \/>\na. Graph quadrilateral KLMN with vertices K(-3, 2), L(2, 2), M(0, -3), and N(-4, 0) on the coordinate grid.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 3\" width=\"295\" height=\"305\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Question 8.<br \/>\nb. On the same coordinate grid, graph the image of quadrilateral KLMN after a translation of 3 units to the right and 4 units up.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-8100\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-1-297x300.gif\" alt=\"grade 8 chapter 9 image 1\" width=\"297\" height=\"300\" \/><\/p>\n<p>Question 8.<br \/>\nc. Which side of the image is congruent to side \\(\\overline { LM } \\)?<br \/>\n___________<br \/>\nName three other pairs of congruent sides.<br \/>\n___________<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nLine LM is congruent to Line L!M!<br \/>\nLine KL is equal to K&#8217;L&#8217;<br \/>\nLine MN is equal to M&#8217;N&#8217;<br \/>\nLine KN is equal to K&#8217;N&#8217;<\/p>\n<p><strong>Draw the image of the figure after each translation.<\/strong><\/p>\n<p>Question 9.<br \/>\n4 units left and 2 units down<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 4\" width=\"300\" height=\"296\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter translation<br \/>\nP'(-3, 1)<br \/>\nQ'(0, 2)<br \/>\nR'(0, -1)<br \/>\nS'(-3, -3)<\/p>\n<p>Question 10.<br \/>\n5 units right and 3 units up<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 5\" width=\"296\" height=\"286\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter translation<br \/>\nA'(0, 4)<br \/>\nB'(3, 5)<br \/>\nC'(3, 1)<br \/>\nD'(0, 0)<\/p>\n<h3><a id=\"Properties_of_Translations_Lesson_Check_\u2013_Page_No._284\"><\/a>Properties of Translations &#8211; Page No. 284<\/h3>\n<p>Question 11.<br \/>\nThe figure shows the ascent of a hot air balloon. How would you describe the translation?<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 6\" width=\"269\" height=\"273\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n4 units along positive X and 5 units along positive Y<\/p>\n<p>Explanation:<br \/>\nInitial coordinate of balloon = ( -2 , -4)<br \/>\nFinal coordinates of the balloon = (2,1)<br \/>\nTranslation along x-axis = 2 &#8211; (-2)<br \/>\n= 4 units along positive x direction<br \/>\nTranslation along y-axis = 1-(-4)<br \/>\n= 5 units along the positive y direction<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168501\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-284-Q12.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 284 Q12\" width=\"575\" height=\"315\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-284-Q12.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-284-Q12-300x164.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 13.<br \/>\na. Multistep Graph triangle XYZ with vertices X(-2, -5), Y(2, -2), and Z(4, -4) on the coordinate grid.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 7\" width=\"292\" height=\"289\" \/><\/p>\n<p>Question 13.<br \/>\nb. On the same coordinate grid, graph and label triangle X&#8217;Y&#8217;Z&#8217;, the image of triangle XYZ after a translation of 3 units to the left and 6 units up.<\/p>\n<p>Question 13.<br \/>\nc. Now graph and label triangle X&#8221;Y&#8221;Z&#8221;, the image of triangle X&#8217;Y&#8217;Z&#8217; after a translation of 1 unit to the left and 2 units down.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8102\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-2.gif\" alt=\"grade 8 chapter 9 image 2\" width=\"257\" height=\"259\" \/><\/p>\n<p>Question 13.<br \/>\nd. Analyze Relationships How would you describe the translation that maps triangle XYZ onto triangle X&#8221;Y&#8221;Z&#8221;?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTriangle XYZ has translated 4 units up and 4 units to the left<\/p>\n<p>Question 14.<br \/>\nCritical Thinking The figure shows rectangle P&#8217;Q&#8217;R&#8217;S&#8217;, the image of rectangle PQRS after a translation of 5 units to the right and 7 units up. Graph and label the preimage PQRS.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 1: Properties of Translations img 8\" width=\"305\" height=\"292\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-3.gif\" alt=\"grade 8 chapter 9 image 3\" width=\"257\" height=\"254\" \/><\/p>\n<p>Question 15.<br \/>\nCommunicate Mathematical Ideas Explain why the image of a figure after a translation is congruent to its preimage.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA translation is a geometric transformation that moves every point of a figure or space by the same amount in a given direction. So the 2 figures are identical and the translated figure is congruent to its pre-image.<\/p>\n<h3><a id=\"Properties_of_Reflections_\u2013_Page_No._288\"><\/a>Guided Practice &#8211; Properties of Reflections &#8211; Page No. 288<\/h3>\n<p>Question 1.<br \/>\nVocabulary A reflection is a transformation that flips a figure across a line called the __________ .<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nReflection Axis<\/p>\n<p>Explanation:<br \/>\nA reflection is a transformation that flips a figure across a line called the Reflection Axis.<\/p>\n<p>Question 2.<br \/>\nThe figure shows trapezoid ABCD.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 9\" width=\"292\" height=\"292\" \/><br \/>\na. Graph the image of the trapezoid after a reflection across the x-axis. Label the vertices of the image.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA'(-3, -4)<br \/>\nB'(1, -4)<br \/>\nC'(3, -1)<br \/>\nD'(-3, -1)<\/p>\n<p>Question 2.<br \/>\nb. How do trapezoid ABCD and trapezoid A&#8217;B&#8217;C&#8217;D&#8217; compare?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ncongruent<\/p>\n<p>Explanation:<br \/>\ntrapezoid ABCD and trapezoid A&#8217;B&#8217;C&#8217;D&#8217; are congruent<\/p>\n<p>Question 2.<br \/>\nc. What If? Suppose you reflected trapezoid ABCD across the y-axis. How would the orientation of the image of the trapezoid compare with the orientation of the preimage?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe orientation would be reversed horizontally.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168503\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-288-Q3.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 288 Q3\" width=\"499\" height=\"234\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-288-Q3.png 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-288-Q3-300x141.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<h3><a id=\"Properties_of_Reflections_\u2013_Page_No._289\"><\/a>9.2 Independent Practice &#8211; Properties of Reflections &#8211; Page No. 289<\/h3>\n<p><strong>The graph shows four right triangles. Use the graph for Exercises 4-7.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 10\" width=\"284\" height=\"286\" \/><\/p>\n<p>Question 4.<br \/>\nWhich two triangles are reflections of each other across the x-axis?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTriangles A and C are the reflections of each other across the x-axis.<\/p>\n<p>Question 5.<br \/>\nFor which two triangles is the line of reflection the y-axis?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFor triangle C &amp; D the line of reflection is y-axis.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168504\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q6.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 289 Q6\" width=\"577\" height=\"395\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q6.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q6-300x205.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168505\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q7.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 289 Q7\" width=\"604\" height=\"323\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q7.png 604w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-289-Q7-300x160.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 8.<br \/>\na. Graph quadrilateral WXYZ with vertices W(-2, -2), X(3, 1), Y(5, -1), and Z(4, -6) on the coordinate grid.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Question 8.<br \/>\nb. On the same coordinate grid, graph quadrilateral W&#8217;X&#8217;Y&#8217;Z&#8217;, the image of quadrilateral WXYZ after a reflection across the x-axis.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-8125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-4-298x300.gif\" alt=\"grade 8 chapter 9 image 4\" width=\"298\" height=\"300\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-4-298x300.gif 298w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-4-150x150.gif 150w\" sizes=\"(max-width: 298px) 100vw, 298px\" \/><\/p>\n<p>Question 8.<br \/>\nc. Which side of the image is congruent to side \\(\\overline { YZ } \\)?<br \/>\n_______________<br \/>\nName three other pairs of congruent sides.<br \/>\n_______________<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nLine YZ = Line Y&#8217;Z&#8217;<br \/>\nLine WX = Line W&#8217;X&#8217;<br \/>\nLine XY = Line X&#8217;Y&#8217;<br \/>\nLine WZ = Line W&#8217;Z&#8217;<\/p>\n<p>Question 8.<br \/>\nd. Which angle of the image is congruent to \u2220X?<br \/>\n_______________<br \/>\nName three other pairs of congruent angles.<br \/>\n_______________<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAngle X&#8217;<br \/>\nAngle W and Angle W&#8217;<br \/>\nAngle Y and Angle Y&#8217;<br \/>\nAngle Z and Angle Z&#8217;<\/p>\n<h3><a id=\"Properties_of_Reflections_Lesson_Check_\u2013_Page_No._290\"><\/a>Properties of Reflections &#8211; Page No. 290<\/h3>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168506\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-290-Q9.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 290 Q9\" width=\"614\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-290-Q9.png 614w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-290-Q9-300x191.png 300w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 10.<br \/>\na. Graph the image of the figure shown after a reflection across the y-axis.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 2: Properties of Reflections img 11\" width=\"262\" height=\"256\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8128\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-5.gif\" alt=\"grade 8 chapter 9 image 5\" width=\"261\" height=\"266\" \/><\/p>\n<p>Question 10.<br \/>\nb. On the same coordinate grid, graph the image of the figure you drew in part a after a reflection across the x-axis.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8129\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-6.gif\" alt=\"grade 8 chapter 9 image 6\" width=\"266\" height=\"268\" \/><\/p>\n<p>Question 10.<br \/>\nc. Make a Conjecture What other sequence of transformations would produce the same final image from the original preimage? Check your answer by performing the transformations. Then make a conjecture that generalizes your findings.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe same image can be obtained by reflecting first across the x-axis and then across the y-axis.<br \/>\nReflecting a figure first across the y-axis and then across the x-axis has the same outcome,. reflecting first across the x-axis and then across the y-axis.<\/p>\n<p>Question 11.<br \/>\na. Graph triangle DEF with vertices D(2, 6), E(5, 6), and F(5, 1) on the coordinate grid.<\/p>\n<p>Question 11.<br \/>\nb. Next graph triangle D \u2032E \u2032F \u2032, the image of triangle DEF after a reflection across the y-axis.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Question 11.<br \/>\nc. On the same coordinate grid, graph triangle D\u2032\u2032 E\u2032\u2032 F\u2032\u2032, the image of triangle D \u2032E \u2032F \u2032 after a translation of 7 units down and 2 units to the right.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-8130\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-7-297x300.gif\" alt=\"grade 8 chapter 9 image 7\" width=\"297\" height=\"300\" \/><\/p>\n<p>Question 11.<br \/>\nd. Analyze Relationships Find a different sequence of transformations that will transform triangle DEF to triangle D \u2032\u2032E \u2032\u2032F \u2032\u2032.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTranslate triangle DEF 7 units down and 2 units to the left. Then reflect the image across the y-axis.<\/p>\n<h3><a id=\"Properties_of_Reflections_Lesson_Check_1_\u2013_Page_No._294\"><\/a>Guided Practice &#8211; Properties of Reflections &#8211; Page No. 294<\/h3>\n<p>Question 1.<br \/>\nVocabulary A rotation is a transformation that turns a figure around a given _____ called the center of rotation.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\npoint<\/p>\n<p>Explanation:<br \/>\nA rotation is a transformation that turns a figure around a given point called the center of rotation.<\/p>\n<p><strong>Siobhan rotates a right triangle 90\u00b0 counterclockwise about the origin.<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168507\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q2.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 294 Q2\" width=\"612\" height=\"257\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q2.png 612w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q2-300x126.png 300w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168508\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q3.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 294 Q3\" width=\"583\" height=\"293\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q3.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-294-Q3-300x151.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p><strong>Draw the image of the figure after the given rotation about the origin.<\/strong><\/p>\n<p>Question 4.<br \/>\n90\u00b0 counterclockwise<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 12\" width=\"258\" height=\"215\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-8133\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-8-300x284.png\" alt=\"grade 8 chapter 9 image 8\" width=\"300\" height=\"284\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-8-300x284.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-8.png 593w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\n180\u00b0<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 13\" width=\"253\" height=\"218\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter 180\u00b0 rotation<br \/>\nA'(-2, -3)<br \/>\nB'(-4, -1)<br \/>\nC'(-2, 0)<br \/>\nD'(0, -1)<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 6.<br \/>\nWhat are the properties of rotations?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nRotations preserve size and shape but change orientation.<\/p>\n<h3><a id=\"Properties_of_Reflections_Lesson_Check_2_\u2013_Page_No._295\"><\/a>9.3 Independent Practice &#8211; Properties of Reflections &#8211; Page No. 295<\/h3>\n<p>Question 7.<br \/>\nThe figure shows triangle ABC and a rotation of the triangle about the origin.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 14\" width=\"254\" height=\"252\" \/><br \/>\na. How would you describe the rotation?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nABC was rotated 90\u00ba counterclockwise about the origin<\/p>\n<p>Question 7.<br \/>\nb. What are the coordinates of the image?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA'(3, 1)<br \/>\nB'(2, 3)<br \/>\nC'(-1, 4)<\/p>\n<p>Question 8.<br \/>\nThe graph shows a figure and its image after a transformation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 15\" width=\"283\" height=\"145\" \/><br \/>\na. How would you describe this as a rotation?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe figure was rotated 180\u00ba about the origin.<\/p>\n<p>Question 8.<br \/>\nb. Can you describe this as a transformation other than a rotation? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nThis can also be described as a reflection across the y-axis.<\/p>\n<p>Question 9.<br \/>\nWhat type of rotation will preserve the orientation of the H-shaped figure in the grid?<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 16\" width=\"184\" height=\"174\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA 180\u00ba rotation about the origin will preserve the orientation of the H-shaped figure in the grid.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168509\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-295-Q10.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 295 Q10\" width=\"601\" height=\"285\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-295-Q10.png 601w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-295-Q10-300x142.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p><strong>Complete the table with rotations of 180\u00b0 or 90\u00b0. Include the direction of rotation for rotations of 90\u00b0.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 17\" width=\"596\" height=\"150\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-8138\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-10-300x64.jpg\" alt=\"grade 8 chapter 9 image 10\" width=\"300\" height=\"64\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-10-300x64.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-10.jpg 585w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><a id=\"Properties_of_Reflections_Lesson_Check_3_\u2013_Page_No._296\"><\/a>Properties of Reflections &#8211; Page No. 296<\/h3>\n<p><strong>Draw the image of the figure after the given rotation about the origin.<\/strong><\/p>\n<p>Question 14.<br \/>\n180\u00b0<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 18\" width=\"258\" height=\"250\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter 180\u00b0<br \/>\nA'(4, 0)<br \/>\nB'(2, -1)<br \/>\nC'(0, 0)<br \/>\nD'(2, 1)<\/p>\n<p>Question 15.<br \/>\n270\u00b0 counterclockwise<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 19\" width=\"250\" height=\"249\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter 270\u00ba counterclockwise rotation<br \/>\nA'(1, 2)<br \/>\nB'(2, -1)<br \/>\nC'(4, 2)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168510\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-296-Q16.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 296 Q16\" width=\"608\" height=\"375\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-296-Q16.png 608w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-296-Q16-300x185.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 17.<br \/>\nProblem Solving Lucas is playing a game where he has to rotate a figure for it to fit in an open space. Every time he clicks a button, the figure rotates 90 degrees clockwise. How many times does he need to click the button so that each figure returns to its original orientation?<br \/>\nFigure A ____________<br \/>\nFigure B ____________<br \/>\nFigure C ____________<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 3: Properties of Rotation img 20\" width=\"246\" height=\"125\" \/><br \/>\nFigure A: _________ time(s)<br \/>\nFigure B: _________ time(s)<br \/>\nFigure C: _________ time(s)<\/p>\n<p>Answer:<br \/>\nFigure A: 2 time(s)<br \/>\nFigure B: 1 time(s)<br \/>\nFigure C: 4 time(s)<\/p>\n<p>Explanation:<br \/>\n2 times to return to original orientation<br \/>\n1 time to return to original orientation<br \/>\n4 times to return to original orientation<\/p>\n<p>Question 18.<br \/>\nMake a Conjecture Triangle ABC is reflected across the y-axis to form the image A\u2032B\u2032C\u2032. Triangle A\u2032B\u2032C\u2032 is then reflected across the x-axis to form the image A\u2033B\u2033C\u2033. What type of rotation can be used to describe the relationship between triangle A\u2033B\u2033C\u2033 and triangle ABC?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTriangle A&#8217;B&#8217;C&#8217; is a 90\u00ba rotation of triangle ABC<br \/>\nTriangle A&#8221;B&#8221;C&#8221; is a 90\u00ba rotation of triangle A&#8217;B&#8217;C&#8217;<br \/>\nTherefore, Triangle A&#8221;B&#8221;C&#8221; is a 180\u00ba rotation of triangle ABC<\/p>\n<p>Question 19.<br \/>\nCommunicate Mathematical Ideas Point A is on the y-axis. Describe all possible locations of image A\u2032 for rotations of 90\u00b0, 180\u00b0, and 270\u00b0. Include the origin as a possible location for A.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIf Point A is on the y-axis, Point A&#8217; will be on the x-axis for 190\u00b0 and 270\u00b0 rotations and on the y-axis for 180\u00b0 rotation<br \/>\nIf point A is at the origin,<br \/>\nA&#8217; is at the origin for any rotation about the origin.<\/p>\n<h3><a id=\"Algebraic_Representations_of_Transformations_\u2013_Page_No._300\"><\/a>Guided Practice &#8211; Algebraic Representations of Transformations &#8211; Page No. 300<\/h3>\n<p>Question 1.<br \/>\nTriangle XYZ has vertices X(-3, -2), Y(-1, 0), and Z(1, -6). Find the vertices of triangle X\u2032Y\u2032Z\u2032 after a translation of 6 units to the right. Then graph the triangle and its image.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 21\" width=\"249\" height=\"259\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter a translation of 6 units to the right:<br \/>\nX'(3, -2)<br \/>\nY'(5, 0)<br \/>\nZ'(7, -6)<\/p>\n<p>Question 2.<br \/>\nDescribe what happens to the x- and y-coordinates after a point is reflected across the x-axis.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe x-coordinate remains the same, while the sign of the y-coordinate changes<\/p>\n<p>Question 3.<br \/>\nUse the rule (x, y) \u2192 (y, -x) to graph the image of the triangle at right. Then describe the transformation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 22\" width=\"249\" height=\"211\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe triangle is rotated 90\u00ba clockwise about the origin<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168511\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-300-Q4.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 300 Q4\" width=\"631\" height=\"226\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-300-Q4.png 631w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-300-Q4-300x107.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><\/p>\n<h3><a id=\"Algebraic_Representations_of_Transformations_\u2013_Page_No._301\"><\/a>9.4 Independent Practice &#8211; Algebraic Representations of Transformations &#8211; Page No. 301<\/h3>\n<p><strong>Write an algebraic rule to describe each transformation. Then describe the transformation.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 23\" width=\"256\" height=\"248\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nalgebraic rule<br \/>\n(x, y) -&gt; (x-2, y-5)<br \/>\ntransformation<br \/>\ntranslation of 2 units to the left and 5 units down<br \/>\nnew coordinates<br \/>\nM'(-4, -2)<br \/>\nN'(-2, -2)<br \/>\nO'(-1, -4)<br \/>\nP'(-4, -4)<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 24\" width=\"265\" height=\"260\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nalgebraic rule<br \/>\n(x, y) -&gt; (-x, -y)<br \/>\ntransformation<br \/>\nrotation of 180\u00ba<br \/>\nnew coordinates<br \/>\nA'(0, 0)<br \/>\nB'(0, -3)<br \/>\nC'(2, -3)<br \/>\nD'(2, 0)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168512\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q7.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 301 Q7\" width=\"653\" height=\"305\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q7.png 653w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q7-300x140.png 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168513\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q8.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 301 Q8\" width=\"619\" height=\"441\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q8.png 619w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-301-Q8-300x214.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><\/p>\n<p>Question 9.<br \/>\nUse the rule (x, y) \u2192 (x &#8211; 2, y &#8211; 4) to graph the image of the rectangle. Then describe the transformation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 25\" width=\"288\" height=\"291\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe rectangle is translated 2 units to the left and 4 units down<\/p>\n<p>Question 10.<br \/>\nParallelogram ABCD has vertices A(\u22122, \u22125\\(\\frac{1}{2}\\)), B(\u22124, \u22125\\(\\frac{1}{2}\\)),C(-3, -2), and D(-1, -2). Find the vertices of parallelogram A\u2032B\u2032C\u2032D\u2032 after a translation of 2 \\(\\frac{1}{2}\\) units down.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nafter a translation of 2 \\(\\frac{1}{2}\\) units<br \/>\nA'(-2, -8)<br \/>\nB'(-4, -8)<br \/>\nC'(-3, -4 \\(\\frac{1}{2}\\))<br \/>\nD'(-1, -4 \\(\\frac{1}{2}\\))<\/p>\n<h3><a id=\"Algebraic_Representations_of_Transformations_Lesson_Check_\u2013_Page_No._302\"><\/a>Algebraic Representations of Transformations &#8211; Page No. 302<\/h3>\n<p>Question 11.<br \/>\nAlexandra drew the logo shown on half-inch graph paper. Write a rule that describes the translation Alexandra used to create the shadow on the letter A.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 26\" width=\"214\" height=\"214\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(x,y) &#8211;&gt; (x+1,y-0.5)<br \/>\n(x+1,y-0.5) &#8211;&gt; (x+0.5,y-0.25)<\/p>\n<p>Explanation:<br \/>\ntranslation in units<br \/>\n(x,y) &#8211;&gt; (x+1,y-0.5)<br \/>\nThis step converts translation rule in units to translation rule in inches. (Divide by 2 since graph paper is half inch paper.<br \/>\n(x+1,y-0.5) &#8211;&gt; (x+0.5,y-0.25)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168514\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q12.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 302 Q12\" width=\"626\" height=\"373\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q12.png 626w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q12-300x179.png 300w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/><\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 13.<br \/>\nMake a Conjecture Graph of the triangle with vertices (-3, 4), (3, 4), and (-5, -5). Use the transformation (y, x) to graph its image.<br \/>\na. Which vertex of the image has the same coordinates as a vertex of the original figure? Explain why this is true.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 4: Algebraic Representations of Transformations img 27\" width=\"233\" height=\"230\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(-5, 5) has the same coordinates<\/p>\n<p>Question 13.<br \/>\nb. What is the equation of a line through the origin and this point?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx and y are equal so switching x and y has no effect on the coordinates<\/p>\n<p>Question 13.<br \/>\nc. Describe the transformation of the triangle.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nx and y are equal so switching x and y has no effect on the coordinates<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168515\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q14.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 302 Q14\" width=\"684\" height=\"576\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q14.png 684w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-302-Q14-300x253.png 300w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><\/p>\n<p>Question 15.<br \/>\nAnalyze Relationships Triangle ABC with vertices A(-2, -2), B(-3, 1), and C(1, 1) is translated by (x, y) \u2192 (x &#8211; 1, y + 3). Then the image, triangle A\u2032B\u2032C\u2032, is translated by (x, y) \u2192 (x + 4, y &#8211; 1), resulting in A\u2033B\u2033C\u2033.<br \/>\na. Find the coordinates for the vertices of triangle A\u2033B\u2033C\u2033.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA&#8221;(-2-1+4, -2+3-1) = A&#8221;(1, 0)<br \/>\nB&#8221;(-3-1+4, 1+3-1) = B&#8221;(0, 3)<br \/>\nC&#8221;(1-1+4, 1+3-1) = C&#8221;(4, 3)<\/p>\n<p>Question 15.<br \/>\nb. Write a rule for one translation that maps triangle ABC to triangle A\u2033B\u2033C\u2033.<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\n(x, y) -&gt; (x-1+4, y+3-1)<br \/>\n(x, y) -&gt; (x+3, y+2)<\/p>\n<h3><a id=\"Congruent_Figures_\u2013_Page_No._306\"><\/a>Guided Practice &#8211; Congruent Figures &#8211; Page No. 306<\/h3>\n<p>Question 1.<br \/>\nApply the indicated series of transformations to the rectangle. Each transformation is applied to the image of the previous transformation, not the original figure. Label each image with the letter of the transformation applied.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 28\" width=\"287\" height=\"297\" \/><br \/>\nA. Reflection across the y-axis<br \/>\nB. Rotation 90\u00b0 clockwise around the origin<br \/>\nC. (x, y) \u2192 (x &#8211; 2, y)<br \/>\nD. Rotation 90\u00b0 counterclockwise around the origin<br \/>\nE. (x, y) \u2192 (x &#8211; 7, y &#8211; 2)<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nA. After transformation<br \/>\n(1, 3)<br \/>\n(1, 4)<br \/>\n(4, 4)<br \/>\n(4, 3)<br \/>\nB. After transformation<br \/>\n(3, -1)<br \/>\n(4, -1)<br \/>\n(4, -4)<br \/>\n(3, -4)<br \/>\nC. After transformation<br \/>\n(1, -1)<br \/>\n(2, -1)<br \/>\n(2, -4)<br \/>\n(1, -4)<br \/>\nD. After transformation<br \/>\n(1, 1)<br \/>\n(1, 2)<br \/>\n(4, 2)<br \/>\n(4, 1)<br \/>\nE. After transformation<br \/>\n(-6, -1)<br \/>\n(-6, 0)<br \/>\n(-3, 0)<br \/>\n(-3, -1)<\/p>\n<p><strong>Identify a sequence of transformations that will transform figure A into figure C.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 29\" width=\"235\" height=\"208\" \/><\/p>\n<p>Question 2.<br \/>\nWhat transformation is used to transform figure A into figure B?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nReflection across the y-axis<\/p>\n<p>Explanation:<br \/>\nReflection across the y-axis is used to transform figure A into figure B<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168516\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q3.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 306 Q3\" width=\"610\" height=\"305\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q3.png 610w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q3-300x150.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168517\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q4.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 306 Q4\" width=\"594\" height=\"493\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q4.png 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q4-300x249.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168518\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q5.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 306 Q5\" width=\"668\" height=\"224\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q5.png 668w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-306-Q5-300x101.png 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 6.<br \/>\nAfter a sequence of translations, reflections, and rotations, what is true about the first figure and the final figure?<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nAfter a sequence of translations, reflections, and rotations, the first and final figures have the same size and shape. (They are congruent)<\/p>\n<h3><a id=\"Congruent_Figures_\u2013_Page_No._307\"><\/a>9.5 Independent Practice &#8211; Congruent Figures &#8211; Page No. 307<\/h3>\n<p><strong>For each given figure A, graph figures B and C using the given sequence of transformations. State whether figures A and C have the same or different orientation.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 30\" width=\"308\" height=\"310\" \/><br \/>\nFigure B: a translation of 1 unit to the right and 3 units up<br \/>\nFigure C: a 90\u00b0 clockwise rotation around the origin<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDifferent orientation<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-11.gif\" alt=\"grade 8 chapter 9 image 11\" width=\"243\" height=\"244\" \/><br \/>\nDifferent orientation<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-31.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 31\" width=\"310\" height=\"306\" \/><br \/>\nFigure B: a reflection across the y-axis<br \/>\nFigure C: a 180\u00b0 rotation around the origin<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDifferent orientation<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-12.gif\" alt=\"grade 8 chapter 9 image 12\" width=\"241\" height=\"243\" \/><br \/>\nDifferent orientation<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-32.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 32\" width=\"310\" height=\"311\" \/><br \/>\nFigure B: a reflection across the y-axis<br \/>\nFigure C: a translation 2 units down<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDifferent orientation<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-13.gif\" alt=\"grade 8 chapter 9 image 13\" width=\"245\" height=\"247\" \/><br \/>\nDifferent orientation<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-33.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 33\" width=\"309\" height=\"313\" \/><br \/>\nFigure B: a translation 2 units up<br \/>\nFigure C: a rotation of 180\u00b0 around the origin<br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nDifferent orientation<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-8195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-9-image-14.gif\" alt=\"grade 8 chapter 9 image 14\" width=\"248\" height=\"249\" \/><br \/>\nDifferent orientation<\/p>\n<h3><a id=\"Congruent_Figures_Lesson_Check_\u2013_Page_No._308\"><\/a>Congruent Figures &#8211; Page No. 308<\/h3>\n<p>Question 11.<br \/>\nRepresent Real-World Problems A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. What transformations were applied to the building at site A to relocate the building to site B? Did the mayor change the size or orientation of the library?<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-34.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 34\" width=\"251\" height=\"227\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFrom Site A to Site B: Translation 2 units right and 4 units down<br \/>\nThe size did NOT change<br \/>\nThe orientation changed<\/p>\n<p>Question 12.<br \/>\nPersevere in Problem-Solving Find a sequence of three transformations that can be used to obtain figure D from figure A. Graph the figures B and C that are created by the transformations.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-35.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Lesson 5: Congruent Figures img 35\" width=\"263\" height=\"262\" \/><br \/>\nType below:<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFrom figure A to D:<br \/>\nReflection across the x-axis (-1, -5) (-1, -6) (2, -5) (4, -6)<br \/>\n90\u00ba clockwise rotation (4, -1) (5, -1) (5, -4) (4, -6)<br \/>\ntranslation 6 units left (4, -1) (5, -1) (5, -4) (4, -6)<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168519\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-308-Q13.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 308 Q13\" width=\"660\" height=\"628\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-308-Q13.png 660w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-308-Q13-300x285.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>Question 14.<br \/>\nMultiple Representations For each representation, describe a possible sequence of transformations.<br \/>\na. (x, y) \u2192 (-x &#8211; 2, y + 1)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ntranslation 2 units right and 1 unit up<br \/>\nreflection across y-axis<\/p>\n<p>Question 14.<br \/>\nb. (x, y) \u2192 (y, -x &#8211; 3)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nrotation 90\u00ba clockwise around the origin<br \/>\ntranslation 3 units down<\/p>\n<h3><a id=\"Model_Quiz_\u2013_Page_No._309\"><\/a>Ready to Go On? &#8211; Model Quiz &#8211; Page No. 309<\/h3>\n<p><strong>9.1\u20139.3 Properties of Translations, Reflections, and Rotations<\/strong><\/p>\n<p>Question 1.<br \/>\nGraph the image of triangle ABC after a translation of 6 units to the right and 4 units down. Label the vertices of the image A\u2019, B\u2019, and C\u2019.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-36.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Model Quiz img 36\" width=\"250\" height=\"258\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter translation:<br \/>\nA'(2, 1)<br \/>\nB'(2, -1)<br \/>\nC'(5, -1)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168520\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q2.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 309 Q2\" width=\"642\" height=\"354\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q2.png 642w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q2-300x165.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p>Question 3.<br \/>\nGraph the image of HIJK after it is rotated 180\u00b0 about the origin. Label the vertices of the image H\u2019I\u2019J\u2019K\u2019.<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-37.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Model Quiz img 37\" width=\"249\" height=\"245\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter rotation:<br \/>\nH'(0, -4)<br \/>\nI'(0, -1)<br \/>\nJ'(2, -2)<br \/>\nK'(2, -3)<\/p>\n<p><strong>9.4 Algebraic Representations of Transformations<\/strong><\/p>\n<p>Question 4.<br \/>\nA triangle has vertices at (2, 3), (\u22122, 2), and (\u22123, 5). What are the coordinates of the vertices of the image after the translation (x, y) \u2192 (x + 4, y \u2212 3)?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter translation:<br \/>\n(6, 0)<br \/>\n(2, -1)<br \/>\n(1, 2)<\/p>\n<p><strong>9.5 Congruent Figures<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168521\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q5.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 309 Q5\" width=\"628\" height=\"323\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q5.png 628w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q5-300x154.png 300w\" sizes=\"(max-width: 628px) 100vw, 628px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168522\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q6.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 309 Q6\" width=\"683\" height=\"395\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q6.png 683w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q6-300x173.png 300w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/p>\n<p><strong>ESSENTIAL QUESTION<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-168523\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q7.png\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Page 309 Q7\" width=\"693\" height=\"299\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q7.png 693w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2022\/05\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-Page-309-Q7-300x129.png 300w\" sizes=\"(max-width: 693px) 100vw, 693px\" \/><\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._310\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 310<\/h3>\n<p>Question 1.<br \/>\nWhat would be the orientation of figure L after a translation of 8 units to the right and 3 units up?<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-38.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Mixed Review img 38\" width=\"331\" height=\"217\" \/><br \/>\nOptions:<br \/>\na. A<br \/>\nb. B<br \/>\nc. C<br \/>\nd. D<\/p>\n<p>Answer:<br \/>\nc. C<\/p>\n<p>Explanation:<br \/>\nAfter a translation of 8 units right and 3 units up, the orientation of figure L stays the same.<\/p>\n<p>Question 2.<br \/>\nFigure A is reflected over the y-axis and then lowered to 6 units. Which sequence describes these transformations?<br \/>\nOptions:<br \/>\na. (x, y) -&gt; (x, -y) and (x, y) -&gt; (x, y &#8211; 6)<br \/>\nb. (x, y) -&gt; (-x, y) and (x, y) -&gt; (x, y &#8211; 6)<br \/>\nc. (x, y) -&gt; (x, -y) and (x, y) -&gt; (x &#8211; 6, y)<br \/>\nd. (x, y) -&gt; (-x, y) and (x, y) -&gt; (x &#8211; 6, y)<\/p>\n<p>Answer:<br \/>\nb. (x, y) -&gt; (-x, y) and (x, y) -&gt; (x, y &#8211; 6)<\/p>\n<p>Explanation:<br \/>\nreflection over the y-axis:<br \/>\n(x, y) -&gt; (-x, y)<br \/>\nTranslation 6 units down<br \/>\n(x, y) -&gt; (x, y-6)<\/p>\n<p>Question 3.<br \/>\nWhat quadrant would the triangle be in after a rotation of 90\u00b0 counterclockwise about the origin?<br \/>\n<img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence-img-39.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence Mixed Review img 39\" width=\"223\" height=\"162\" \/><br \/>\nOptions:<br \/>\na. I<br \/>\nb. II<br \/>\nc. III<br \/>\nd. IV<\/p>\n<p>Answer:<br \/>\nd. IV<\/p>\n<p>Explanation:<br \/>\nAfter a rotation of 90\u00b0 counterclockwise about the origin, the triangle will be in QIV<\/p>\n<p>Question 4.<br \/>\nWhich rational number is greater than \u22123 \\(\\frac{1}{3}\\) but less than \u2212\\(\\frac{4}{5}\\)?<br \/>\nOptions:<br \/>\na. \u22120.4<br \/>\nb. \u2212\\(\\frac{9}{7}\\)<br \/>\nc. \u22120.19<br \/>\nd. \u2212\\(\\frac{22}{5}\\)<\/p>\n<p>Answer:<br \/>\nb. \u2212\\(\\frac{9}{7}\\)<\/p>\n<p>Question 5.<br \/>\nWhich of the following is not true of a trapezoid that has been reflected across the x-axis?<br \/>\nOptions:<br \/>\na. The new trapezoid is the same size as the original trapezoid.<br \/>\nb. The new trapezoid is the same shape as the original trapezoid.<br \/>\nc. The new trapezoid is in the same orientation as the original trapezoid.<br \/>\nd. The x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.<\/p>\n<p>Answer:<br \/>\nd. The x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.<\/p>\n<p>Explanation:<br \/>\nThe x-coordinates of the new trapezoid are the same as the x-coordinates of the original trapezoid.<\/p>\n<p>Question 6.<br \/>\nA triangle with coordinates (6, 4), (2, \u22121), and (\u22123, 5) is translated 4 units left and rotated 180\u00b0 about the origin. What are the coordinates of its image?<br \/>\nOptions:<br \/>\na. (2, 4), (-2, -1), (-7, 5)<br \/>\nb. (4, 6), (-1, 2), (5, -3)<br \/>\nc. (4, -2), (-1, 2), (5, 7)<br \/>\nd. (-2, -4), (2, 1), (7, -5)<\/p>\n<p>Answer:<br \/>\nd. (-2, -4), (2, 1), (7, -5)<\/p>\n<p>Question 7.<br \/>\nA rectangle with vertices (3, -2), (3, -4), (7, -2), (7, -4) is reflected across the x-axis and then rotated 90\u00b0 counterclockwise.<br \/>\na. In what quadrant does the image lie?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nAfter reflection and rotation, the image lies in QII<\/p>\n<p>Question 7.<br \/>\nb. What are the vertices of the image?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nimage vertices<br \/>\n(-2, 3)<br \/>\n(-4, 3)<br \/>\n(-2, 7)<br \/>\n(-4, 7)<\/p>\n<p>Question 7.<br \/>\nc. What other transformations produce the same image?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA reflection across the y-axis and 90\u00ba\u00a0clockwise rotation will produce the same result.<\/p>\n<h3>Conclusion:<\/h3>\n<p>The Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence pdf are available both online and offline. We have provided in pdf format so that students can practice the problems offline. We know that maths is the scoring and also typical among all the subjects. But you can make it easy if you understand the concept of the chapter. Students can refer to the Go Math Grade 8 Answer Key in their convenient way. Practice well and make maths your favorite subject. Best of Luck!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are multiple ways to learn maths. But choosing the best material is also important for the students to score good marks and also to improve their knowledge. This will be possible only with the help of our Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence. You can get the explanation for &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/go-math-grade-8-answer-key-chapter-9-transformations-and-congruence\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 9 Transformations and Congruence\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":168615,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2023\/02\/Go-Math-Grade-8-Answer-Key-Chapter-9-Transformations-and-Congruence.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/6669"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=6669"}],"version-history":[{"count":3,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/6669\/revisions"}],"predecessor-version":[{"id":168524,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/6669\/revisions\/168524"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/168615"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=6669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=6669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=6669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}