Lesson 9.3 - Rotations Standard G.2.4

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.

Rotation on A Graph… 3 Types of rotations… 1. 900 (x, y) (-y, x) 2. 1800 (x, y) (-x, -y) 3. 2700 (x, y) (y, -x)

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

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

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)

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

Practice Worksheet 9.3