Chapter 9.3 Notes: Perform Reflections

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Presentation transcript:

Chapter 9.3 Notes: Perform Reflections Goal: You will reflect a figure in any given line.

A reflection is a transformation that uses a line like a mirror to reflect an image. The mirror line is called the line of reflection. Ex.1: The vertices of ΔABC are A(-3, 2), B(-4, 5), and C(-2, 6). Reflect ΔABC in the y-axis. Ex.2: The vertices of ΔABC are A(1, 3), B(5, 2), and C(2, 1). Graph the reflection of ΔABC described. a. In the line x = 3 b. In the line y = 1

Theorem 9.2 Reflection Theorem: A reflection is an isometry. Coordinate Rules for Reflections: If (a, b) is reflected in the line y = x, its image is the point (b, a). If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).

Ex. 3: The endpoints of FG are F(-1, 2) and G(1, 2) Ex.3: 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. Ex.4: Graph ΔABC with vertices A(1, 3), B(4, 4), and C(3, 1). Reflect ΔABC in the line y = -x. Graph each image. Ex.5: The vertices of ΔDEF are D(0, 2), E(1, 4), and F(3, 1). Reflect ΔDEF in the line x = 4, and then reflect ΔD’E’F’ in the line y = -2.

Ex. 6: The vertices of ΔPQR are P(-3, 6), Q(-5, 3), and R(-1, 2) Ex.6: The vertices of ΔPQR are P(-3, 6), Q(-5, 3), and R(-1, 2). Reflect ΔPQR in the line y = x, and then reflect ΔP’Q’R’ in the line y = -10.