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.

2 Topics For Today… 1.) You should be able to perform a 900 rotation in the coordinate plane using double reflections 2.) You should be able to perform double reflections and then tell me what rotation occurred.

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

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

Rotation on A Graph… A 900 rotation always involves 2 steps: Step 1: Reflect across the line y = x. This means trade the x and y places Change the signs so that the rotated points will end up in the correct quadrant

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

You Try This One…. D(4, 1) E(-4, -5) F(2, -3) Rotate ΔDEF 900 clockwise if D(4, 1), E(-4, -5), and F(2, -3) D(4, 1) E(-4, -5) F(2, -3) D’(1, -4) Quad 1 goes to Quad 4 D’ F’ E’ D F E E’(-5, 4) Quad 3 goes to Quad 2 F’(-3, -2) Quad 4 goes to Quad 3

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’ D’(4, -1), E’(-4, 5), F’(2, 3) D F E Now change the x signs to reflect across the y-axis D’(-4, -1), E’(4, 5), F’(-2, 3) 1800 Rotation Occurred

Practice Worksheet 9.3