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10. Rectangle ABCD with vertices A(1, 0), B(7, 2), C(8, -1), and D(2, -3): O (a) Translation: (x, y)→ (x-8, y-3) (b) Reflection: in the x-axis 71 432654 1 ܩܠܕ ܚ ܚ ܠ ܬ ܗ ܢ -2 0-3 -4 -5 -7-6-5-4-3-2— 2 3 4 5 6 7 A -6 -7 4 O O Plot both (a) and (b) points A"- Bª CH- D" 111

10. Rectangle ABCD with vertices A(1, 0), B(7, 2), C(8, -1), and D(2, -3): O (a) Translation: (x, y)→ (x-8, y-3) (b) Reflection: in the x-axis 71 432654 1 ܩܠܕ ܚ ܚ ܠ ܬ ܗ ܢ -2 0-3 -4 -5 -7-6-5-4-3-2— 2 3 4 5 6 7 A -6 -7 4 O O Plot both (a) and (b) points A"- Bª CH- D" 111

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Geometry Transformations: Translation and Reflection** **Problem 10: Rectangle Transformations** Consider rectangle \(ABCD\) with the vertices: - \(A(1, 0)\) - \(B(7, 2)\) - \(C(8, -1)\) - \(D(2, -3)\) **Transformations:** 1. **Translation:** Move each point using the translation rule \((x, y) \rightarrow (x - 8, y - 3)\). 2. **Reflection:** Reflect each translated point over the x-axis. **Instructions:** - **Plot the Transformed Points:** Determine the coordinates of the rectangle after each transformation, and complete the plotting on the provided graph. - **Record Coordinates:** Fill in the coordinates of the transformed points \(A''\), \(B''\), \(C''\), and \(D''\). **Graph Details:** - The graph includes axes ranging from \(-7\) to \(7\) on both x and y. - Circles indicate grid points for easy plotting. - A red box highlights the plotting area. **Tasks:** - **Plot and Analyze:** Use the given transformations to plot the new positions on the graph. Observe how the rectangle shifts and flips. - **Complete the Table:** - \(A''(\_\_,\_\_)\) - \(B''(\_\_,\_\_)\) - \(C''(\_\_,\_\_)\) - \(D''(\_\_,\_\_)\) Understanding these transformations is crucial for grasping the concepts of geometry transformations, exploring changes in position, orientation, and reflection across coordinates.
Transcribed Image Text:**Geometry Transformations: Translation and Reflection** **Problem 10: Rectangle Transformations** Consider rectangle \(ABCD\) with the vertices: - \(A(1, 0)\) - \(B(7, 2)\) - \(C(8, -1)\) - \(D(2, -3)\) **Transformations:** 1. **Translation:** Move each point using the translation rule \((x, y) \rightarrow (x - 8, y - 3)\). 2. **Reflection:** Reflect each translated point over the x-axis. **Instructions:** - **Plot the Transformed Points:** Determine the coordinates of the rectangle after each transformation, and complete the plotting on the provided graph. - **Record Coordinates:** Fill in the coordinates of the transformed points \(A''\), \(B''\), \(C''\), and \(D''\). **Graph Details:** - The graph includes axes ranging from \(-7\) to \(7\) on both x and y. - Circles indicate grid points for easy plotting. - A red box highlights the plotting area. **Tasks:** - **Plot and Analyze:** Use the given transformations to plot the new positions on the graph. Observe how the rectangle shifts and flips. - **Complete the Table:** - \(A''(\_\_,\_\_)\) - \(B''(\_\_,\_\_)\) - \(C''(\_\_,\_\_)\) - \(D''(\_\_,\_\_)\) Understanding these transformations is crucial for grasping the concepts of geometry transformations, exploring changes in position, orientation, and reflection across coordinates.
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