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
**Reflect Across the x-axis** The given diagram shows a triangle on a coordinate grid. The triangle is labeled with vertices A, B, and C. The coordinates for each point are approximately as follows: - Point A is at (-3, 0) - Point B is at (-2, 3) - Point C is at (3, 1) The grid is divided into equal squares with the x-axis and y-axis intersecting at the origin (0,0). The scales on the axes are consistent, with each square representing one unit. To reflect this triangle across the x-axis, follow these steps: 1. **Identify the reflection rule**: When reflecting a point (x, y) across the x-axis, its image will be at (x, -y). 2. **Apply the rule to each vertex**: - Reflect A: (-3, 0) remains (-3, 0) since it lies on the x-axis. - Reflect B: (-2, 3) becomes (-2, -3). - Reflect C: (3, 1) becomes (3, -1). 3. **Plot the reflected points**: Once the new positions of A, B, and C are calculated, plot them on the coordinate plane. 4. **Draw the reflected triangle**: Connect the reflected points to form the reflected triangle, which mirrors the original triangle across the x-axis. The reflection will result in a triangle that is an exact mirror image of the original triangle, across the x-axis.
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Transcribed Image Text:**Reflect Across the x-axis** The given diagram shows a triangle on a coordinate grid. The triangle is labeled with vertices A, B, and C. The coordinates for each point are approximately as follows: - Point A is at (-3, 0) - Point B is at (-2, 3) - Point C is at (3, 1) The grid is divided into equal squares with the x-axis and y-axis intersecting at the origin (0,0). The scales on the axes are consistent, with each square representing one unit. To reflect this triangle across the x-axis, follow these steps: 1. **Identify the reflection rule**: When reflecting a point (x, y) across the x-axis, its image will be at (x, -y). 2. **Apply the rule to each vertex**: - Reflect A: (-3, 0) remains (-3, 0) since it lies on the x-axis. - Reflect B: (-2, 3) becomes (-2, -3). - Reflect C: (3, 1) becomes (3, -1). 3. **Plot the reflected points**: Once the new positions of A, B, and C are calculated, plot them on the coordinate plane. 4. **Draw the reflected triangle**: Connect the reflected points to form the reflected triangle, which mirrors the original triangle across the x-axis. The reflection will result in a triangle that is an exact mirror image of the original triangle, across the x-axis.
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