1. MA 08 transformations 2.3 Reflections

2. 10/7/20152.3 Reflections2 Topic/Objectives Reflection Identify and use reflections in a plane. Understand Line Symmetry Essential Question: How can you reflect over a line?

3. 10/7/20152.3 Reflections3 Reflection A reflection in line m is a transformation that maps every point P in the plane to point P’ so the following properties are true: Line of Reflection m P P’ P and P’ are equidistant from line m.

4. 10/7/20152.3 Reflections4 Reflections on the Coordinate Plane Graph the reflection of A(2, 3) in the x-axis. 3 3 A’(2, -3) A(2, 3)  A’(2, -3) A Reflection in the x-axis has the mapping: (x, y)  (x, -y)

5. 10/7/20152.3 Reflections5 Reflections on the Coordinate Plane Graph the reflection of A(2, 3) in the y-axis. 22 A’(-2, 3) A(2, 3)  A’(-2, 3) A Reflection in the y-axis has the mapping: (x, y)  (-x, y)

6. 10/7/20152.3 Reflections6 Reflections on the Coordinate Plane Graph the reflection of A(1, 4) in the line y = x. A’(4, 1) A(1, 4)  A’(4, 1) A Reflection in the line y = x has the mapping: (x, y)  (y, x)

7. 10/7/20152.3 Reflections7 Reflection Mappings In the x-axis: (x, y)  (x, -y) In the y-axis: (x, y)  (-x, y) In y = x: (x, y)  (y, x) We say: Reflect in the x-axis, reflect over the x-axis, reflect on the x-axis, reflect across the x-axis. They mean the same thing.

8. 10/7/20152.3 Reflections8 Reflect  RST in y-axis. R S T Determine coordinates. Mapping Formula: (x, y)  (-x, y) R(0, 4)  R’(0, 4) S(-4, 1)  S’(4, 1) T(-1, -2)  T’(1, -2) (0, 4) (-4, 1) (-1, -2) T’(1, -2) S’(4, 1) R’(0, 4)

9. 10/7/20152.3 Reflections9 Reflect ABCD in the x-axis. Mapping Formula: (x, y)  (x, -y) A(-2, 2)  A’(-2, -2) B(-3, -1)  B’(-3, 1) C(3, -1)  C’(3, 1) D(2, 2)  D’(2, -2) A(-2, 2) B(-3, -1)C(3, -1) D(2, 2)

10. 10/7/20152.3 Reflections10 Reflect AB on the line x = 2. A(1, 3) B(0, 1) A’(3, 3) B’(4, 1)