Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
**Rotation and Translation of Triangles** In the diagram shown, triangle \( \triangle JKL \) has been rotated 270° counterclockwise about point \( J \), resulting in triangle \( \triangle J'K'L' \). **Graph Explanation:** - The graph is a coordinate plane with the x-axis and y-axis ranging from -8 to 8. - The original triangle \( \triangle JKL \) has the following coordinates: \( J (1, 2) \), \( K (4, 1) \), and \( L (4, 4) \). - After the rotation, the new triangle \( \triangle J'K'L' \) is formed at the coordinates: \( J' (1, 2) \), \( K' (2, -1) \), and \( L' (-1, -1) \). - A second triangle \( \triangle RST \) is shown in red, with coordinates \( R (2, -3) \), \( S (5, -4) \), and \( T (5, -7) \). **Translation Task:** The task is to determine the rule that will translate triangle \( \triangle J'K'L' \) onto triangle \( \triangle RST \). **Graph Elements:** - Points are represented as filled circles. - Vectors connect the vertices of each triangle. - \(\triangle JKL\) and \(\triangle J'K'L'\) are in black, while \(\triangle RST\) is in red. **Interactive Components:** - There are dropdown menus below the graph to select transformation rules for both x and y coordinates. **Problem-Solving Strategy:** To find the translation rule, observe the horizontal and vertical shifts needed to align corresponding points of \( J' \) with \( R \), \( K' \) with \( S \), and \( L' \) with \( T \). Analyze changes in x and y coordinates accordingly.
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Transcribed Image Text:**Rotation and Translation of Triangles** In the diagram shown, triangle \( \triangle JKL \) has been rotated 270° counterclockwise about point \( J \), resulting in triangle \( \triangle J'K'L' \). **Graph Explanation:** - The graph is a coordinate plane with the x-axis and y-axis ranging from -8 to 8. - The original triangle \( \triangle JKL \) has the following coordinates: \( J (1, 2) \), \( K (4, 1) \), and \( L (4, 4) \). - After the rotation, the new triangle \( \triangle J'K'L' \) is formed at the coordinates: \( J' (1, 2) \), \( K' (2, -1) \), and \( L' (-1, -1) \). - A second triangle \( \triangle RST \) is shown in red, with coordinates \( R (2, -3) \), \( S (5, -4) \), and \( T (5, -7) \). **Translation Task:** The task is to determine the rule that will translate triangle \( \triangle J'K'L' \) onto triangle \( \triangle RST \). **Graph Elements:** - Points are represented as filled circles. - Vectors connect the vertices of each triangle. - \(\triangle JKL\) and \(\triangle J'K'L'\) are in black, while \(\triangle RST\) is in red. **Interactive Components:** - There are dropdown menus below the graph to select transformation rules for both x and y coordinates. **Problem-Solving Strategy:** To find the translation rule, observe the horizontal and vertical shifts needed to align corresponding points of \( J' \) with \( R \), \( K' \) with \( S \), and \( L' \) with \( T \). Analyze changes in x and y coordinates accordingly.
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