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Reflection and Graphing of Line Segments in Coordinate Geometry

Explore the reflection of line segments in the coordinate plane, focusing on the line y = x and y = -x. This guide provides examples of reflecting points and segments, demonstrating how to graph their images accurately. Learn the rules of reflection, the importance of slopes in determining perpendicularity, and the step-by-step process of graphing segments and their reflections. Practice by reflecting triangle ABC with given vertices and verifying the relationships of slopes in reflections.

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Reflection and Graphing of Line Segments in Coordinate Geometry

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  1. The endpoints of FG are F(–1, 2) and G(1, 2). Reflect the segment in the line y = x. Graph the segment and its image. EXAMPLE 2 Graph a reflection in y = x

  2. The slope of GG′ will also be –1. From G, move 0.5 units right and 0.5 units down to y = x. Then move 0.5 units right and 0.5 units down to locate G′(2, 1). The slope of y = xis 1. The segment from Fto its image, FF ′ , is perpendicular to the line of reflection y = x, so the slope of FF ′ will be –1 (because 1(–1) = –1). FromF, move 1.5 units right and 1.5 units down to y = x. From that point, move 1.5 units right and 1.5 units down to locateF′(2,–1). EXAMPLE 2 Graph a reflection in y = x SOLUTION

  3. Reflect FGfrom Example 2 in the line y = –x. Graph FGand its image. (a, b) (–b, –a) F(–1, 2) F ′(–2, 1) G(1, 2) G ′(–2, –1) EXAMPLE 3 Graph a reflection in y = –x SOLUTION Use the coordinate rule for reflecting in y = –x.

  4. SOLUTION for Examples 2 and 3 GUIDED PRACTICE Graph ABC with vertices A(1, 3), B(4, 4), and C(3, 1). Reflect ABC in the lines y = –x and y = x. Graph each image.

  5. Slope of y = – xis –1. The slope of FF′ is 1. The product of their slopes is –1 making them perpendicular. for Examples 2 and 3 GUIDED PRACTICE ′ 5. In Example 3, verify that FF is perpendicular to y = –x. SOLUTION

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