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Translate the image by the directed line segment from (0,0) to (4,1).

Translate the image by the directed line segment from (0,0) to (4,1).

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 of Geometric Figures Translate the image by the directed line segment from \((0,0)\) to \((4,1)\). #### Given Points: - \( A = (-2, 5) \) - \( B = (-6, -2) \) - \( C = (-1, -2) \) ### Task: Determine the new coordinates for points \(A\), \(B\), and \(C\) after translation by the vector \((4, 1)\). #### Steps: 1. Add the translation vector \((4, 1)\) to each original coordinate. 2. For point \(A\): \[ A' = A + (4,1) = (-2+4, 5+1) = (2, 6) \] 3. For point \(B\): \[ B' = B + (4,1) = (-6+4, -2+1) = (-2, -1) \] 4. For point \(C\): \[ C' = C + (4,1) = (-1+4, -2+1) = (3, -1) \] ### Translated Coordinates: - \( A' = (2, 6) \) - \( B' = (-2, -1) \) - \( C' = (3, -1) \) #### Graph Explanation: The graph provided consists of a coordinate plane with both the x-axis and the y-axis ranging from -10 to 10. The original triangle \( \triangle ABC \) is plotted with vertices at: - \( A(-2, 5) \) - \( B(-6, -2) \) - \( C(-1, -2) \) To translate this triangle, each vertex is moved 4 units right and 1 unit up, as indicated by the directed line segment from the origin \((0,0)\) to the point \((4,1)\). This method demonstrates how to shift all points of a geometric figure by the same amount in a given direction, effectively translating the entire figure.
Transcribed Image Text:### Translation of Geometric Figures Translate the image by the directed line segment from \((0,0)\) to \((4,1)\). #### Given Points: - \( A = (-2, 5) \) - \( B = (-6, -2) \) - \( C = (-1, -2) \) ### Task: Determine the new coordinates for points \(A\), \(B\), and \(C\) after translation by the vector \((4, 1)\). #### Steps: 1. Add the translation vector \((4, 1)\) to each original coordinate. 2. For point \(A\): \[ A' = A + (4,1) = (-2+4, 5+1) = (2, 6) \] 3. For point \(B\): \[ B' = B + (4,1) = (-6+4, -2+1) = (-2, -1) \] 4. For point \(C\): \[ C' = C + (4,1) = (-1+4, -2+1) = (3, -1) \] ### Translated Coordinates: - \( A' = (2, 6) \) - \( B' = (-2, -1) \) - \( C' = (3, -1) \) #### Graph Explanation: The graph provided consists of a coordinate plane with both the x-axis and the y-axis ranging from -10 to 10. The original triangle \( \triangle ABC \) is plotted with vertices at: - \( A(-2, 5) \) - \( B(-6, -2) \) - \( C(-1, -2) \) To translate this triangle, each vertex is moved 4 units right and 1 unit up, as indicated by the directed line segment from the origin \((0,0)\) to the point \((4,1)\). This method demonstrates how to shift all points of a geometric figure by the same amount in a given direction, effectively translating the entire figure.
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