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Graph triangle LMN with L(2, 7), M(8, 8), N(2, 1), and its image after Ry-axis ° T(-4,-5).

Graph triangle LMN with L(2, 7), M(8, 8), N(2, 1), and its image after Ry-axis ° T(-4,-5).

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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**Educational Content: Understanding Transformations in Geometry** **Problem Description**: You are given triangle LMN with the following vertices: - L(2, 7) - M(8, 8) - N(2, 1) Apply the transformation \( R_{y-axis} \circ T_{<-4,-5>} \) to the triangle and determine the new coordinates of point N', the image of point N after the transformation. **Transformation Explanation**: 1. **Translation \( T_{<-4,-5>} \)**: - Move each point of the triangle left by 4 units and down by 5 units. - For point N(2, 1): - New x-coordinate: \( 2 - 4 = -2 \) - New y-coordinate: \( 1 - 5 = -4 \) - Resulting point after translation: N'(-2, -4) 2. **Reflection Across the Y-axis \( R_{y-axis} \)**: - Reflect the point over the y-axis, meaning the x-coordinate changes sign while the y-coordinate remains the same. - For point N'(-2, -4) after translation: - Reflected x-coordinate: \( -(-2) = 2 \) - Y-coordinate remains: -4 - Resulting point after reflection: N'(2, -4) **Solution**: - The coordinates of N' after the transformations are (2, -4). **Important Concepts**: - **Translation** involves moving every point of a shape a certain distance in a specific direction. - **Reflection** is flipping a shape over a line, such as the y-axis, which changes the sign of the x-coordinate but keeps the y-coordinate the same. By understanding these transformations, you can accurately determine the new positions of geometric figures on the coordinate plane.
Transcribed Image Text:**Educational Content: Understanding Transformations in Geometry** **Problem Description**: You are given triangle LMN with the following vertices: - L(2, 7) - M(8, 8) - N(2, 1) Apply the transformation \( R_{y-axis} \circ T_{<-4,-5>} \) to the triangle and determine the new coordinates of point N', the image of point N after the transformation. **Transformation Explanation**: 1. **Translation \( T_{<-4,-5>} \)**: - Move each point of the triangle left by 4 units and down by 5 units. - For point N(2, 1): - New x-coordinate: \( 2 - 4 = -2 \) - New y-coordinate: \( 1 - 5 = -4 \) - Resulting point after translation: N'(-2, -4) 2. **Reflection Across the Y-axis \( R_{y-axis} \)**: - Reflect the point over the y-axis, meaning the x-coordinate changes sign while the y-coordinate remains the same. - For point N'(-2, -4) after translation: - Reflected x-coordinate: \( -(-2) = 2 \) - Y-coordinate remains: -4 - Resulting point after reflection: N'(2, -4) **Solution**: - The coordinates of N' after the transformations are (2, -4). **Important Concepts**: - **Translation** involves moving every point of a shape a certain distance in a specific direction. - **Reflection** is flipping a shape over a line, such as the y-axis, which changes the sign of the x-coordinate but keeps the y-coordinate the same. By understanding these transformations, you can accurately determine the new positions of geometric figures on the coordinate plane.
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