{"id":83661,"date":"2022-06-01T16:39:56","date_gmt":"2022-06-01T11:09:56","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=83661"},"modified":"2022-05-10T14:19:41","modified_gmt":"2022-05-10T08:49:41","slug":"eureka-math-grade-8-module-3-lesson-5","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-3-lesson-5\/","title":{"rendered":"Eureka Math Grade 8 Module 3 Lesson 5 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 3 Lesson 5 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 3 Lesson 5 Exercise Answer Key<\/h3>\n

Exercise 1.
\nIn the diagram below, points P and Q have been dilated from center O by scale factor r. \\(\\overline{P Q}\\) || \\(\\overline{\\boldsymbol{P}^{\\prime} \\boldsymbol{Q}^{\\prime}}\\) |PQ|=5 cm, and |P’Q’|=10 cm.
\n\"Eureka<\/p>\n

b. Determine the scale factor r.
\nAnswer:
\nAccording to FTS, |P’Q’|=r|PQ|. Therefore, 10=r\u22195, so r=2.<\/p>\n

b. Locate the center O of dilation. Measure the segments to verify that |OP’|=r|OP| and |OQ’|=r|OQ|. Show your work below.
\nAnswer:
\nCenter O and measurements are shown above.
\n|OP’|=r|OP|
\n6=2\u22193
\n6=6
\n|OQ’|=r|OQ|
\n8=2\u22194
\n8=8<\/p>\n

Exercise 2.
\nIn the diagram below, you are given center O and ray \\(\\overrightarrow{0 A}\\). Point A is dilated by a scale factor r=4. Use what you know about FTS to find the location of point A’.
\n\"Eureka
\nAnswer:
\nPoint A’ must be located at (12,12).<\/p>\n

Exercise 3.
\nIn the diagram below, you are given center O and ray \\(\\overrightarrow{0 A}\\). Point A is dilated by a scale factor r=\\(\\frac{5}{12}\\). Use what you know about FTS to find the location of point A’.
\n\"Eureka
\nAnswer:
\nThe x-coordinate of A’ is 5. The y-coordinate is equal to the length of segment A’B’. Since |A’B’|=r|AB|, then |A’B’|=\\(\\frac{5}{12}\\)\u22198=\\(\\frac{40}{12}\\)\u22483.3. The location of A’ is (5,3.3).<\/p>\n

Eureka Math Grade 8 Module 3 Lesson 5 Exit Ticket Answer Key<\/h3>\n

In the diagram below, you are given center O and ray \\(\\overrightarrow{O A}\\). Point A is dilated by a scale factor r= \\(\\frac{6}{4}\\). Use what you know about FTS to find the location of point A’.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nThe y-coordinate of A’ is 6. The x-coordinate is equal to the length of segment A’B’. Since |A’B’|=r|AB|, then
\n|A’B’|=\\(\\frac{6}{4}\\)\u22193=\\(\\frac{18}{4}\\)=4.5. The location of A’ is (4.5,6).<\/p>\n

Eureka Math Grade 8 Module 3 Lesson 5 Problem Set Answer Key<\/h3>\n

Students practice using the first consequences of FTS in terms of dilated points and their locations on the coordinate plane.<\/p>\n

Question 1.
\nDilate point A, located at (3,4) from center O, by a scale factor r=\\(\\frac{5}{3}\\).
\n\"Eureka
\nWhat is the precise location of point A’?
\nAnswer:
\nThe y-coordinate of point A’ is the length of segment A’B’. Since |A’B’|=r|AB|, then |A’B’|=\\(\\frac{5}{3}\\)\u22194=\\(\\frac{20}{3}\\). The location of point A’ is
\n(5,\\(\\frac{20}{3}\\)), or approximately (5,6.7).<\/p>\n

Question 2.
\nDilate point A, located at (9,7) from center O, by a scale factor r=\\(\\frac{4}{9}\\). Then, dilate point B, located at (9,5) from center O, by a scale factor of r=\\(\\frac{4}{9}\\). What are the coordinates of points A’ and B’? Explain.
\n\"Eureka
\nAnswer:
\nThe y-coordinate of point A’ is the length of A’C’. Since |A’C’|=r|AC|, then |A’C’|=\\(\\frac{4}{9}\\)\u22197=\\(\\frac{28}{9}\\). The location of point A’ is (4, \\(\\frac{28}{9}\\)), or approximately (4,3.1). The y-coordinate of point B’ is the length of B’C’. Since |B’C’|=r|BC|, then |B’C’|=\\(\\frac{4}{9}\\)\u22195=\\(\\frac{20}{9}\\). The location of point B’ is (4, \\(\\frac{20}{9}\\)), or approximately (4,2.2).<\/p>\n

Question 3.
\nExplain how you used the fundamental theorem of similarity in Problems 1 and 2.
\nAnswer:
\nUsing what I knew about scale factor, I was able to determine the placement of points A’ and B’, but I did not know the actual coordinates. So, one of the ways that FTS was used was actually in terms of the converse of FTS. I had to make sure I had parallel lines. Since the lines of the coordinate plane guarantee parallel lines, I knew that |A’C’|=r|AC|. Then, since I knew the length of segment AC and the scale factor, I could find the precise location of A’. The precise location of B’ was found in a similar way but using |B’C’|=r|BC|.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 3 Lesson 5 Answer Key Eureka Math Grade 8 Module 3 Lesson 5 Exercise Answer Key Exercise 1. In the diagram below, points P and Q have been dilated from center O by scale factor r. || |PQ|=5 cm, and |P’Q’|=10 cm. b. Determine the scale factor r. … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/83661"}],"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=83661"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/83661\/revisions"}],"predecessor-version":[{"id":137259,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/83661\/revisions\/137259"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=83661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=83661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=83661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}