Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**11. Sakura rotated polygon \(ABC\) 180° clockwise about the origin. The following figure shows her work. Is Sakura's work correct? Justify your answer.** **Diagram Explanation:** The image contains two triangles on a coordinate plane. - **Triangle \(ABC\):** This is the original triangle with vertices labeled \(A\), \(B\), and \(C\). The coordinates before rotation are shown in the negative x-positive y quadrant. - **Triangle \(A'B'C'\):** This is the rotated image of triangle \(ABC\). Its vertices, labeled \(A'\), \(B'\), and \(C'\), are in the positive x-negative y quadrant. **Graph Description:** - The x and y axes are shown with markings at intervals of one unit. - Both triangles are drawn with their vertices connected by lines forming the triangle shape. - The rotation appears to have been performed around the origin (0,0). **Analysis:** For a 180° clockwise rotation about the origin, the coordinates of each point \((x, y)\) should be transformed to \((-x, -y)\). To verify Sakura's work, compare the coordinates of each vertex before and after rotation: - If \(A (x_1, y_1)\) becomes \(A' (-x_1, -y_1)\), and similarly for \(B\) and \(C\), the work is correct. Review the specific coordinates of each point to ensure this transformation.
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Transcribed Image Text:**11. Sakura rotated polygon \(ABC\) 180° clockwise about the origin. The following figure shows her work. Is Sakura's work correct? Justify your answer.** **Diagram Explanation:** The image contains two triangles on a coordinate plane. - **Triangle \(ABC\):** This is the original triangle with vertices labeled \(A\), \(B\), and \(C\). The coordinates before rotation are shown in the negative x-positive y quadrant. - **Triangle \(A'B'C'\):** This is the rotated image of triangle \(ABC\). Its vertices, labeled \(A'\), \(B'\), and \(C'\), are in the positive x-negative y quadrant. **Graph Description:** - The x and y axes are shown with markings at intervals of one unit. - Both triangles are drawn with their vertices connected by lines forming the triangle shape. - The rotation appears to have been performed around the origin (0,0). **Analysis:** For a 180° clockwise rotation about the origin, the coordinates of each point \((x, y)\) should be transformed to \((-x, -y)\). To verify Sakura's work, compare the coordinates of each vertex before and after rotation: - If \(A (x_1, y_1)\) becomes \(A' (-x_1, -y_1)\), and similarly for \(B\) and \(C\), the work is correct. Review the specific coordinates of each point to ensure this transformation.
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