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Draw the image of quadrilateral ABCD under the translation (x,y) → (x-7, y+1). - Y

Draw the image of quadrilateral ABCD under the translation (x,y) → (x-7, y+1). - Y

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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**Transcription and Explanation for Educational Website** --- **Title: Translating a Quadrilateral on the Coordinate Plane** **Instruction:** Draw the image of quadrilateral \(ABCD\) under the translation \((x, y) \rightarrow (x-7, y+1)\). **Graph Explanation:** - The graph is a coordinate plane with axes labeled \(x\) and \(y\), ranging from -7 to 7 on both axes. - A light grid pattern covers the entire plane to assist with plotting points and shapes. - The quadrilateral \(ABCD\) is plotted on the plane. **Initial Quadrilateral \(ABCD\):** - Points are approximately at: - \(A(1, 1)\) - \(B(1, 4)\) - \(C(4, 4)\) - \(D(4, 1)\) - This quadrilateral is shaded lightly in green and is positioned in the upper right quadrant. **Transformed Quadrilateral \(A'B'C'D'\):** - The translation moves each point 7 units left and 1 unit up: - \(A'(1-7, 1+1) = (-6, 2)\) - \(B'(1-7, 4+1) = (-6, 5)\) - \(C'(4-7, 4+1) = (-3, 5)\) - \(D'(4-7, 1+1) = (-3, 2)\) - The transformed quadrilateral is plotted and shaded in blue, positioned in the lower left quadrant. **Conclusion:** This exercise demonstrates how each vertex of a shape on the coordinate plane is altered through translation. Understanding translations is essential for grasping more complex geometrical transformations. Remember to adjust both \(x\) and \(y\) coordinates according to the translation instructions provided. --- This transcription and explanation guide students through the process of performing and visualizing translations in coordinate geometry.
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Title: Translating a Quadrilateral on the Coordinate Plane** **Instruction:** Draw the image of quadrilateral \(ABCD\) under the translation \((x, y) \rightarrow (x-7, y+1)\). **Graph Explanation:** - The graph is a coordinate plane with axes labeled \(x\) and \(y\), ranging from -7 to 7 on both axes. - A light grid pattern covers the entire plane to assist with plotting points and shapes. - The quadrilateral \(ABCD\) is plotted on the plane. **Initial Quadrilateral \(ABCD\):** - Points are approximately at: - \(A(1, 1)\) - \(B(1, 4)\) - \(C(4, 4)\) - \(D(4, 1)\) - This quadrilateral is shaded lightly in green and is positioned in the upper right quadrant. **Transformed Quadrilateral \(A'B'C'D'\):** - The translation moves each point 7 units left and 1 unit up: - \(A'(1-7, 1+1) = (-6, 2)\) - \(B'(1-7, 4+1) = (-6, 5)\) - \(C'(4-7, 4+1) = (-3, 5)\) - \(D'(4-7, 1+1) = (-3, 2)\) - The transformed quadrilateral is plotted and shaded in blue, positioned in the lower left quadrant. **Conclusion:** This exercise demonstrates how each vertex of a shape on the coordinate plane is altered through translation. Understanding translations is essential for grasping more complex geometrical transformations. Remember to adjust both \(x\) and \(y\) coordinates according to the translation instructions provided. --- This transcription and explanation guide students through the process of performing and visualizing translations in coordinate geometry.
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