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What are the vertices of AA'B'C produced by T-3,6, (AABC) AA'B'CT 4 -2 2 O -2 C y A X B

What are the vertices of AA'B'C produced by T-3,6, (AABC) AA'B'CT 4 -2 2 O -2 C y A X B

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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**Understanding Translation of Triangles in a Coordinate Plane** In this problem, we are given a triangle \( \Delta ABC \) in the coordinate plane. We are asked to find the vertices of the image \( \Delta A'B'C' \) of the triangle after it has been translated by the transformation \( T_{(-3, 6)} \). **Graph Explanation:** The graph shows a coordinate plane with triangle \( \Delta ABC \). The vertex coordinates for \( \Delta ABC \) are: - A is located at (1, 2) - B is located at (3, -2) - C is located at (0, -2) We need to apply the transformation \( T_{(-3, 6)} \) to each vertex. This means we will move each point 3 units to the left (negative direction on the x-axis) and 6 units up (positive direction on the y-axis). **Vertices Calculation:** 1. For point A (1, 2): \[ A' = (1 - 3, 2 + 6) = (-2, 8) \] 2. For point B (3, -2): \[ B' = (3 - 3, -2 + 6) = (0, 4) \] 3. For point C (0, -2): \[ C' = (0 - 3, -2 + 6) = (-3, 4) \] **Answer Choices:** - A. \( A'(0, 6), B'(0, 4), C'(-3, 3) \) - B. \( A'(6, 6), B'(6, 4), C'(3, 3) \) - C. \( A'(0, -6), B'(0, -8), C'(-3, 9) \) - D. \( A'(6, -6), B'(6, -8), C'(3, 9) \) After calculating the translated coordinates, the correct option should reflect the coordinates we calculated. Therefore, none of the provided options match the correct translated coordinates \((-2, 8), (0, 4), (-3, 4)\). This problem seems to have incorrect answer choices. **Conclusion:** The calculated vertices of the translated triangle
Transcribed Image Text:**Understanding Translation of Triangles in a Coordinate Plane** In this problem, we are given a triangle \( \Delta ABC \) in the coordinate plane. We are asked to find the vertices of the image \( \Delta A'B'C' \) of the triangle after it has been translated by the transformation \( T_{(-3, 6)} \). **Graph Explanation:** The graph shows a coordinate plane with triangle \( \Delta ABC \). The vertex coordinates for \( \Delta ABC \) are: - A is located at (1, 2) - B is located at (3, -2) - C is located at (0, -2) We need to apply the transformation \( T_{(-3, 6)} \) to each vertex. This means we will move each point 3 units to the left (negative direction on the x-axis) and 6 units up (positive direction on the y-axis). **Vertices Calculation:** 1. For point A (1, 2): \[ A' = (1 - 3, 2 + 6) = (-2, 8) \] 2. For point B (3, -2): \[ B' = (3 - 3, -2 + 6) = (0, 4) \] 3. For point C (0, -2): \[ C' = (0 - 3, -2 + 6) = (-3, 4) \] **Answer Choices:** - A. \( A'(0, 6), B'(0, 4), C'(-3, 3) \) - B. \( A'(6, 6), B'(6, 4), C'(3, 3) \) - C. \( A'(0, -6), B'(0, -8), C'(-3, 9) \) - D. \( A'(6, -6), B'(6, -8), C'(3, 9) \) After calculating the translated coordinates, the correct option should reflect the coordinates we calculated. Therefore, none of the provided options match the correct translated coordinates \((-2, 8), (0, 4), (-3, 4)\). This problem seems to have incorrect answer choices. **Conclusion:** The calculated vertices of the translated triangle
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