1. Lesson Rotations
Standard G.2.4

2. What is a Rotation?
A Rotation like a reflection and translation does not change the shape or the shapes size. It only changes where the shape is facing.

3. Rotation on A Graph… 3 Types of rotations… 1. 900 (x, y) (-y, x)
(x, y) (-x, -y)
(x, y) (y, -x)

4. Example
Rotate ΔABC 900 counterclockwise if A(5, 1), B(3, -2), C(-1, 3)
A(5, 1)
B(3, -2)
C(-1, 3)
A’(-1, 5) A’ B’ C’ A C B
Quad 1 moves to Quad 2
B’(2, 3)
Quad 4 moves to Quad 1
C’(-3, -1)
Quad 2 moves to Quad 3

5. Recall From Last Time… We can reflect points in four different ways
Across the x-axis
All y-values switch signs
Across the y-axis
All x-values switch signs
Across the line y = x
x-values and y-values trade spots
Around the origin
All x-values and y-values switch signs

6. Double Reflections
Reflect ΔDEF if D(4, 1), E(-4, -5), and F(2, -3), First across the x-axis and then across the y-axis. What rotation occurred?
First change all of the y signs to reflect across the x-axis D’ F’ E’
(x, y) (x, -y) D F E
Now change the x signs to reflect across the y-axis
(x, y) (x, -y) (-x, -y)
D’(-4, -1), E’(4, 5), F’(-2, 3)

7. Quadrants of a Graph (-, +) (+, +) (-, -) (+, -) Quadrant 2 Quadrant 1

8. Practice
Worksheet 9.3