{"id":83689,"date":"2022-06-01T16:30:49","date_gmt":"2022-06-01T11:00:49","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=83689"},"modified":"2022-05-10T14:19:41","modified_gmt":"2022-05-10T08:49:41","slug":"eureka-math-grade-8-module-7-lesson-17","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-7-lesson-17\/","title":{"rendered":"Eureka Math Grade 8 Module 7 Lesson 17 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 7 Lesson 17 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 7 Lesson 17 Example Answer Key<\/h3>\n

Example 1.
\nWhat is the distance between the two points A and B on the coordinate plane?
\n\"Engage
\nAnswer:
\nWhat is the distance between the two points A and B on the coordinate plane?
\nThe distance between points A and B is 6 units.<\/p>\n

What is the distance between the two points A and B on the coordinate plane?
\n\"Engage
\nAnswer:
\nWhat is the distance between the two points A and B on the coordinate plane?
\nThe distance between points A and B is 2 units.<\/p>\n

What is the distance between the two points A and B on the coordinate plane? Round your answer to the tenths place.
\n\"Engage
\nAnswer:
\nWhat is the distance between the two points A and B on the coordinate plane? Round your answer to the tenths place.
\nProvide students time to solve the problem. Have students share their work and estimations of the distance between the points. The questions that follow can be used to guide students\u2019 thinking.<\/p>\n

We cannot simply count units between the points because the line that connects A to B is not horizontal or vertical. What have we done recently that allowed us to find the length of an unknown segment?
\n\"Engage
\n\u2192 The Pythagorean theorem allows us to determine the length of an unknown side of a right triangle.
\n\u2192 Use what you know about the Pythagorean theorem to determine the distance between points A and B.
\nProvide students time to solve the problem now that they know that the Pythagorean theorem can help them. If necessary, the questions below can guide students\u2019 thinking.
\nWe must draw a right triangle so that |AB| is the hypotenuse. How can we construct the right triangle that we need?<\/p>\n

\u2192 Draw a vertical line through B and a horizontal line through A. Or, draw a vertical line through A and a horizontal line through B.
\n\"Engage
\nLet\u2019s mark the point of intersection of the horizontal and vertical lines we drew as point C. What is the length of \\(\\overline{A C}\\)? \\(\\overline{B C}\\)?
\n\"Engage
\n|AC| = 6 units, and |BC| = 2 units
\nNow that we know the lengths of the legs of the right triangle, we can determine the length of \\(\\overline{A B}\\).
\nRemind students that because we are finding a length, we need only consider the positive value of the square root because a negative length does not make sense. If necessary, remind students of this fact throughout their work in this lesson.
\nLet c be the length of \\(\\overline{A B}\\).
\n22<\/sup> + 62<\/sup> = c2<\/sup>
\n4 + 36 = c2<\/sup>
\n40 = c2<\/sup>
\n\\(\\sqrt{40}\\) = c
\n6.3 \u2248 c The distance between points A and B is approximately 6.3 units.<\/p>\n

Example 2.
\nGiven two points A and B on the coordinate plane, determine the distance between them. First, make an estimate; then, try to find a more precise answer. Round your answer to the tenths place.
\n\"Engage
\nAnswer:
\nProvide students time to solve the problem. Have students share their work and estimations of the distance between the points. The questions below can be used to guide students\u2019 thinking.
\nWe know that we need a right triangle. How can we draw one?
\n\"Engage
\n\"Engage
\n\u2192 Draw a vertical line through B and a horizontal line through A. Or draw a vertical line through A and a horizontal line through B.
\nMark the point C at the intersection of the horizontal and vertical lines. What do we do next?<\/p>\n

\u2192 Count units to determine the lengths of the legs of the right triangle, and then use the Pythagorean theorem to find |AB|.
\nShow the last diagram, and ask a student to explain the answer.
\n\"Engage
\n|AC| = 3 units, and |BC| = 3 units. Let c be |AB|.
\n32<\/sup> + 32<\/sup> = c2<\/sup>
\n9 + 9 = c2<\/sup>
\n18 = c2<\/sup>
\n\\(\\sqrt{18}\\) = c
\n4.2 \u2248 c
\nThe distance between points A and B is approximately 4.2 units.<\/p>\n

Example 3.
\nIs the triangle formed by the points A, B, C a right triangle?
\n\"Engage
\nAnswer:
\n\u2192How can we verify if a triangle is a right triangle?
\nUse the converse of the Pythagorean theorem.<\/p>\n

\u2192 What information do we need about the triangle in order to use the converse of the Pythagorean theorem, and how would we use it?
\nWe need to know the lengths of all three sides; then, we can check to see if the side lengths satisfy the Pythagorean theorem.
\n\"Engage
\n\u2192 Clearly, |AB| = 10 units. How can we determine |AC|?
\nTo find |AC|, follow the same steps used in the previous problem. Draw horizontal and vertical lines to form a right triangle, and use the Pythagorean theorem to determine the length.
\n\u2192 Determine |AC|. Leave your answer in square root form unless it is a perfect square.
\n\"Engage
\nLet c represent |AC|.
\n12<\/sup> + 32<\/sup> = c2<\/sup>
\n1 + 9 = c2<\/sup>
\n10 = c2<\/sup>
\n\\(\\sqrt{10}\\) = c
\n\"Engage
\nNow, determine |BC|. Again, leave your answer in square root form unless it is a perfect square.
\nLet c represent |BC|.
\n92<\/sup> + 32<\/sup> = c2<\/sup>
\n81 + 9 = c2<\/sup>
\n90 = c2<\/sup>
\n\\(\\sqrt{90}\\) = c
\n\u2192 The lengths of the three sides of the triangle are 10 units, \\(\\sqrt{10}\\) units, and \\(\\sqrt{90}\\) units. Which number represents the hypotenuse of the triangle? Explain.
\nThe side \\(\\overline{A B}\\) must be the hypotenuse because it is the longest side. When estimating the lengths of the other two sides, I know that \\(\\sqrt{10}\\) is between 3 and 4, and \\(\\sqrt{90}\\) is between 9 and 10. Therefore, the side that is 10 units in length is the hypotenuse.<\/p>\n

\u2192 Use the lengths 10, \\(\\sqrt{10}\\), and \\(\\sqrt{90}\\) to determine if the triangle is a right triangle.
\nSample response:
\n(\\(\\sqrt{10}\\))2<\/sup> + (\\(\\sqrt{90}\\))2<\/sup> = 102<\/sup>
\n10 + 90 = 100
\n100 = 100
\nTherefore, the points A, B, C form a right triangle.<\/p>\n

Eureka Math Grade 8 Module 7 Lesson 17 Exercise Answer Key<\/h3>\n

Exercises 1\u20134
\nFor each of the Exercises 1\u20134, determine the distance between points A and B on the coordinate plane. Round your answer to the tenths place.<\/p>\n

Exercise 1.
\n\"Engage
\nAnswer:
\n\"Engage
\nLet c represent |AB|.
\n52<\/sup> + 62<\/sup> = c2<\/sup>
\n25 + 36 = c2<\/sup>
\n61 = c2<\/sup>
\n\\(\\sqrt{61}\\) = c
\n7.8 \u2248 c
\nThe distance between points A and B is about 7.8 units.<\/p>\n

Exercise 2.
\n\"Engage
\nAnswer:
\n\"Engage
\nLet c represent |AB|.
\n132<\/sup> + 42<\/sup> = c2<\/sup>
\n169 + 16 = c2<\/sup>
\n185 = c2<\/sup>
\n\\(\\sqrt{185}\\) = c
\n13.6 \u2248 c
\nThe distance between points A and B is about 13.6 units.<\/p>\n

Exercise 3.
\n\"Engage
\nAnswer:
\n\"Engage
\nLet c represent |AB|.
\n32<\/sup> + 52<\/sup> = c2<\/sup>
\n9 + 25 = c2<\/sup>
\n34 = c2<\/sup>
\n\\(\\sqrt{34}\\) = c
\n5.8 \u2248 c
\nThe distance between points A and B is about 5.8 units.<\/p>\n

Exercise 4.
\n\"Engage
\nAnswer:
\n\"Engage
\nLet c represent |AB|.
\n52<\/sup> + 42<\/sup> = c2<\/sup>
\n25 + 16 = c2<\/sup>
\n41 = c2<\/sup>
\n\\(\\sqrt{41}\\) = c
\n6.4 \u2248 c
\nThe distance between points A and B is about 6.4 units.<\/p>\n

Eureka Math Grade 8 Module 7 Lesson 17 Problem Set Answer Key<\/h3>\n

For each of the Problems 1\u20134, determine the distance between points A and B on the coordinate plane. Round your answer to the tenths place.
\nQuestion 1.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nLet c represent |AB|.
\n62<\/sup> + 72<\/sup> = c2<\/sup>
\n36 + 49 = c2<\/sup>
\n85 = c2<\/sup>
\n\\(\\sqrt{85}\\) = c
\n9.2 \u2248 c
\nThe distance between points A and B is about 9.2 units.<\/p>\n

Question 2.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nLet c represent |AB|.
\n92<\/sup> + 42<\/sup> = c2<\/sup>
\n81 + 16 = c2<\/sup>
\n97 = c2<\/sup>
\n\\(\\sqrt{97}\\) = c
\n9.8 \u2248 c
\nThe distance between points A and B is about 9.8 units.<\/p>\n

Question 3.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nLet c represent |AB|.
\n22<\/sup> + 82<\/sup> = c2<\/sup>
\n4 + 64 = c2<\/sup>
\n68 = c2<\/sup>
\n\\(\\sqrt{68}\\) = c
\n8.2 \u2248 c
\nThe distance between points A and B is about 8.2 units.<\/p>\n

Question 4.
\n\"Eureka
\nAnswer:
\n\"Eureka
\nLet c represent |AB|.
\n112<\/sup> + 42<\/sup> = c2<\/sup>
\n121 + 16 = c2<\/sup>
\n137 = c2<\/sup>
\n\\(\\sqrt{137}\\) = c
\n11.7 \u2248 c
\nThe distance between points A and B is about 11.7 units.<\/p>\n

Question 5.
\nIs the triangle formed by points A, B, C a right triangle?
\n\"Eureka
\nAnswer:
\n\"Eureka
\nLet c represent |AB|.
\n32<\/sup> + 62<\/sup> = c2<\/sup>
\n9 + 36 = c2<\/sup>
\n45 = c2<\/sup>
\n\\(\\sqrt{45}\\) = c<\/p>\n

Let c represent |AC|.
\n32<\/sup> + 52<\/sup> = c2<\/sup>
\n9 + 25 = c2<\/sup>
\n34 = c2<\/sup>
\n\\(\\sqrt{34}\\) = c<\/p>\n

Let c represent |BC|.
\n32<\/sup> + 82<\/sup> = c2<\/sup>
\n9 + 64 = c2<\/sup>
\n73 = c2<\/sup>
\n\\(\\sqrt{73}\\) = c<\/p>\n

(\\(\\sqrt{45}\\))2<\/sup> + (\\(\\sqrt{34}\\))2<\/sup> = (\\(\\sqrt{73}\\))2<\/sup>
\n45 + 34 = 73
\n79 \u2260 73
\nNo, the points do not form a right triangle.<\/p>\n

Eureka Math Grade 8 Module 7 Lesson 17 Exit Ticket Answer Key<\/h3>\n

Use the following diagram to answer the questions below.
\n\"Eureka
\nQuestion 1.
\nDetermine |AC|. Leave your answer in square root form unless it is a perfect square.
\nAnswer:
\nLet c represent |AC|.
\n42<\/sup> + 42<\/sup> = c2<\/sup>
\n16 + 16 = c2<\/sup>
\n32 = c2<\/sup>
\n\\(\\sqrt{32}\\) = c<\/p>\n

Question 2.
\nDetermine |CB|. Leave your answer in square root form unless it is a perfect square.
\nAnswer:
\nLet d represent |CB|.
\n32<\/sup> + 42<\/sup> = d2<\/sup>
\n9 + 16 = d2<\/sup>
\n25 = d2<\/sup>
\n\\(\\sqrt{25}\\) = d
\n5 = d<\/p>\n

Question 3.
\nIs the triangle formed by the points A, B, C a right triangle? Explain why or why not.
\nAnswer:
\nUsing the lengths 5,\\(\\sqrt{32}\\), and |AB| = 7 to determine if the triangle is a right triangle, I have to check to see if
\n52<\/sup> + (\\(\\sqrt{32}\\))2<\/sup> = 72<\/sup>
\n25 + 32 \u2260 49
\nTherefore, the triangle formed by the points A, B, C is not a right triangle because the lengths of the triangle do not satisfy the Pythagorean theorem.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 7 Lesson 17 Answer Key Eureka Math Grade 8 Module 7 Lesson 17 Example Answer Key Example 1. What is the distance between the two points A and B on the coordinate plane? Answer: What is the distance between the two points A and B on the coordinate … 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\/83689"}],"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=83689"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/83689\/revisions"}],"predecessor-version":[{"id":137278,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/83689\/revisions\/137278"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=83689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=83689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=83689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}