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List the coordinates of the pre-image and the image of a reflection about the y=x R 7 x S

List the coordinates of the pre-image and the image of a reflection about the y=x R 7 x S

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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### Problem 5: Coordinate Reflection **Task:** List the coordinates of the pre-image and the image of a reflection about the line \( y = x \). **Graph Explanation:** - The graph consists of a triangle with vertices labeled \( Q \), \( R \), and \( S \). - The triangle is plotted in the first quadrant of the Cartesian plane. - Coordinate values on the graph grid will be used for accuracy. **Vertices and Coordinates:** - **Pre-image Coordinates:** - \( Q \) is located at the origin, \( (0, 0) \). - \( R \) is located at \( (3, 1) \). - \( S \) is located at \( (5, 2) \). **Reflection Across \( y = x \):** - To reflect a point across the line \( y = x \), exchange the x-coordinate and the y-coordinate. - The reflection of \( (x, y) \) is \( (y, x) \). - **Image Coordinates (after reflection):** - \( Q' \) remains \( (0, 0) \) (as reflecting the origin results in no change). - \( R' \) will be \( (1, 3) \). - \( S' \) will be \( (2, 5) \). This process highlights reflecting points across the line \( y = x \) and demonstrates how coordinate values interchange.
Transcribed Image Text:### Problem 5: Coordinate Reflection **Task:** List the coordinates of the pre-image and the image of a reflection about the line \( y = x \). **Graph Explanation:** - The graph consists of a triangle with vertices labeled \( Q \), \( R \), and \( S \). - The triangle is plotted in the first quadrant of the Cartesian plane. - Coordinate values on the graph grid will be used for accuracy. **Vertices and Coordinates:** - **Pre-image Coordinates:** - \( Q \) is located at the origin, \( (0, 0) \). - \( R \) is located at \( (3, 1) \). - \( S \) is located at \( (5, 2) \). **Reflection Across \( y = x \):** - To reflect a point across the line \( y = x \), exchange the x-coordinate and the y-coordinate. - The reflection of \( (x, y) \) is \( (y, x) \). - **Image Coordinates (after reflection):** - \( Q' \) remains \( (0, 0) \) (as reflecting the origin results in no change). - \( R' \) will be \( (1, 3) \). - \( S' \) will be \( (2, 5) \). This process highlights reflecting points across the line \( y = x \) and demonstrates how coordinate values interchange.
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