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Suppose ADEF is the image of a translation of AABC. If D is at (-6, -2), what translation rule maps AABC to ADEF?

Suppose ADEF is the image of a translation of AABC. If D is at (-6, -2), what translation rule maps AABC to ADEF?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Translation/Rotation Quiz: Educational Content #### Question: **Suppose △DEF is the image of a translation of △ABC. If D is at (-6, -2), what translation rule maps △ABC to △DEF?** #### Graph Interpretation: In the provided graph, triangles △ABC and △DEF are illustrated on a coordinate plane. The coordinates for triangle △ABC are as follows: - \( A (1, 1) \) - \( B (3, -1) \) - \( C (2, -2) \) The point \( D \) of triangle △DEF is given at coordinates (-6, -2). The task is to determine the translation rule (T) that maps △ABC to △DEF. #### Answer Options: A. \( T_{0, -2}\)(△ABC) = △DEF B. \( T_{6, -2}\)(△ABC) = △DEF C. \( T_{-9, 2}\)(△ABC) = △DEF D. \( T_{-9, -3}\)(△ABC) = △DEF **Steps for Finding the Correct Translation Rule:** 1. Calculate the vector from point \( A \) of △ABC to point \( D \) of △DEF. - Starting from \( A(1, 1) \) to \( D(-6, -2) \) - Translation vector: \( D - A = (-6 - 1, -2 - 1) = (-7, -3) \) 2. Apply the same translation vector to points \( B \) and \( C \) of △ABC: - For point \( B(3, -1) \): - New coordinates: \( (3 - 7, -1 - 3) = (-4, -4) \) - For point \( C(2, -2) \): - New coordinates: \( (2 - 7, -2 - 3) = (-5, -5) \) 3. Verify if these new coordinates correspond to points E and F of △DEF as per the given graph. Based on the given answer choices, the closest match to the correct translation rule is: \[ T_{-7, -3}\] However, reviewing the given options, there might be a typographical error. The correct answer may not be explicitly listed among the
Transcribed Image Text:### Translation/Rotation Quiz: Educational Content #### Question: **Suppose △DEF is the image of a translation of △ABC. If D is at (-6, -2), what translation rule maps △ABC to △DEF?** #### Graph Interpretation: In the provided graph, triangles △ABC and △DEF are illustrated on a coordinate plane. The coordinates for triangle △ABC are as follows: - \( A (1, 1) \) - \( B (3, -1) \) - \( C (2, -2) \) The point \( D \) of triangle △DEF is given at coordinates (-6, -2). The task is to determine the translation rule (T) that maps △ABC to △DEF. #### Answer Options: A. \( T_{0, -2}\)(△ABC) = △DEF B. \( T_{6, -2}\)(△ABC) = △DEF C. \( T_{-9, 2}\)(△ABC) = △DEF D. \( T_{-9, -3}\)(△ABC) = △DEF **Steps for Finding the Correct Translation Rule:** 1. Calculate the vector from point \( A \) of △ABC to point \( D \) of △DEF. - Starting from \( A(1, 1) \) to \( D(-6, -2) \) - Translation vector: \( D - A = (-6 - 1, -2 - 1) = (-7, -3) \) 2. Apply the same translation vector to points \( B \) and \( C \) of △ABC: - For point \( B(3, -1) \): - New coordinates: \( (3 - 7, -1 - 3) = (-4, -4) \) - For point \( C(2, -2) \): - New coordinates: \( (2 - 7, -2 - 3) = (-5, -5) \) 3. Verify if these new coordinates correspond to points E and F of △DEF as per the given graph. Based on the given answer choices, the closest match to the correct translation rule is: \[ T_{-7, -3}\] However, reviewing the given options, there might be a typographical error. The correct answer may not be explicitly listed among the
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