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

2. 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

3. 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).

4. 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.

5. 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.