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Suppose the triangle in the figure below is reflected in the x-axis. Given the points A(4,2) B(1,5) C(3,7) -10 10 -10 A(4,2) B(1,5) C(3,7) What are the coordinates of the image triangle. A' B'( C(

Suppose the triangle in the figure below is reflected in the x-axis. Given the points A(4,2) B(1,5) C(3,7) -10 10 -10 A(4,2) B(1,5) C(3,7) What are the coordinates of the image triangle. A' B'( C(

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
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**Title: Understanding Reflections in Coordinate Geometry** **Introduction:** In this lesson, we will explore how to reflect a triangle across the x-axis in a coordinate plane. We will use a specific example to illustrate this concept. **Problem Statement:** Suppose the triangle in the figure below is reflected in the x-axis. Given the points: - A(4, 2) - B(1, 5) - C(3, 7) This is the original triangle plotted on a coordinate grid. **Graph Explanation:** The graph shows a coordinate plane with x-axis and y-axis both ranging from -10 to 10. The triangle is located in the first quadrant, formed by the points: - A at (4, 2) - B at (1, 5) - C at (3, 7) Each vertex of the triangle is marked and connected to form the shape. **Reflection Explanation:** When a shape is reflected over the x-axis, the x-coordinates of its vertices stay the same, but the y-coordinates are transformed into their opposites (multiplied by -1). **Steps to Reflect the Triangle:** 1. Reflect point A(4,2): The x-coordinate remains 4, but the y-coordinate becomes -2. Therefore, A' is (4, -2). 2. Reflect point B(1,5): The x-coordinate remains 1, but the y-coordinate becomes -5. Therefore, B' is (1, -5). 3. Reflect point C(3,7): The x-coordinate remains 3, but the y-coordinate becomes -7. Therefore, C' is (3, -7). **New Coordinates:** After reflecting the triangle over the x-axis, the new coordinates of the vertices are: - A'(4, -2) - B'(1, -5) - C'(3, -7) **Reflection Exercise:** Verify your understanding by reflecting the given points and plotting the new triangle on a coordinate plane. **Interactive Section:** _Please enter the coordinates of the image triangle:_ A' (____, ____) B' (____, ____) C' (____, ____) **Conclusion:** Reflecting a shape over the x-axis involves changing the sign of the y-coordinates of all vertices while keeping the x-coordinates unchanged. This transformation helps understand symmetry in coordinate geometry. **Further Reading:** For
Transcribed Image Text:**Title: Understanding Reflections in Coordinate Geometry** **Introduction:** In this lesson, we will explore how to reflect a triangle across the x-axis in a coordinate plane. We will use a specific example to illustrate this concept. **Problem Statement:** Suppose the triangle in the figure below is reflected in the x-axis. Given the points: - A(4, 2) - B(1, 5) - C(3, 7) This is the original triangle plotted on a coordinate grid. **Graph Explanation:** The graph shows a coordinate plane with x-axis and y-axis both ranging from -10 to 10. The triangle is located in the first quadrant, formed by the points: - A at (4, 2) - B at (1, 5) - C at (3, 7) Each vertex of the triangle is marked and connected to form the shape. **Reflection Explanation:** When a shape is reflected over the x-axis, the x-coordinates of its vertices stay the same, but the y-coordinates are transformed into their opposites (multiplied by -1). **Steps to Reflect the Triangle:** 1. Reflect point A(4,2): The x-coordinate remains 4, but the y-coordinate becomes -2. Therefore, A' is (4, -2). 2. Reflect point B(1,5): The x-coordinate remains 1, but the y-coordinate becomes -5. Therefore, B' is (1, -5). 3. Reflect point C(3,7): The x-coordinate remains 3, but the y-coordinate becomes -7. Therefore, C' is (3, -7). **New Coordinates:** After reflecting the triangle over the x-axis, the new coordinates of the vertices are: - A'(4, -2) - B'(1, -5) - C'(3, -7) **Reflection Exercise:** Verify your understanding by reflecting the given points and plotting the new triangle on a coordinate plane. **Interactive Section:** _Please enter the coordinates of the image triangle:_ A' (____, ____) B' (____, ____) C' (____, ____) **Conclusion:** Reflecting a shape over the x-axis involves changing the sign of the y-coordinates of all vertices while keeping the x-coordinates unchanged. This transformation helps understand symmetry in coordinate geometry. **Further Reading:** For
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