# Translations, Rotations, Reflections, and Dilations Transformations: Rotations on a Coordinate Plane Meet TED. TED is going to help us learn about rotations. First lets focus on TEDs eyes. What are the coordinates of his left eye? What are the coordinates of his right eye? Good, now you will need to use those coordinates in order to help you discover to rules for rotations.

Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 4. When we rotate we always go in order of quadrant unless told otherwise. A full rotation is 360 so if you rotate halfway around that would be a _____ rotation. A 90 rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure

90 from quadrant 4 it would then be in quadrant ______. ROTATIONS basic rotations A (-4,2) A (2,4) A ( , ) B (-7,7) B (7,7) B ( , ) C(-3,9) C(9,3) C( , ) Rotations on the Coordinate

Plane Know the formulas for: 90 rotations 180 rotations

clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0,02/23/20 0).

90 clockwise rotation A(-2, 4) Formula (x, y) (y, x) A(4, 2) 02/23/20 Rotate (-3, -2) 90 clockwise

Formula A(-2, 3) (-3, -2) 02/23/20 (x, y) (y, x) 90 counter-clockwise rotation

Formula A(2, 4) (x, y) (y, x) A(4, -2) 02/23/20 Rotate (-5, 3) 90 counterclockwise

Formula (-5, 3) (-3, -5) 02/23/20 (x, y) (y, x) 180 rotation Formula

(x, y) (x, y) A(4, 2) A(-4, -2) 02/23/20 Rotate (3, -4) 180 Formula

(-3, 4) (x, y) (x, y) (3, -4) 02/23/20 Rotation Example Draw a coordinate grid and graph:

B(-2, 4) A(-3, 0) B(-2, 4) A(-3, 0) C(1, -1) C(1, -1)

Draw ABC 02/23/20 Rotation Example B(-2, 4) Rotate ABC 90 clockwise. Formula

A(-3, 0) 02/23/20 C(1, -1) (x, y) (y, x) Rotate ABC 90 clockwise. B(-2, 4)

A B A(-3, 0) C C(1, -1) 02/23/20 (x, y) (y, x)

A(-3, 0) A(0, 3) B(-2, 4) B(4, 2) C(1, -1) C(-1, -1) Rotate ABC 90 clockwise. B(-2, 4) A B

A(-3, 0) C C(1, -1) 02/23/20 Check by rotating ABC 90. Rotation Example Rotate ABC 270

clockwise. B(-2, 4) Formula? A(-3, 0) C(1, -1) We must use the

counterclockwise formula for 90, because 270 clockwise, is the same as 90 counterclockwise. (x, y) (y, x) 02/23/20 Rotate ABC 270 clockwise, or 90 counterclockwise.

B(-2, 4) (x, y) (y, x) A(-3, 0) A(0, -3) C C(1, -1) A(-3, 0) B

02/23/20 B(-2, 4) B(-4, -2) C(1, -1) C(1, 1) A Rotation Formulas

90 CW 90 CCW 180 02/23/20 (x, y) (y, x)

(x, y) (y, x) (x, y) (x, y) http://www.ixl.com/math/g rade-8/rotations-graph-the -image 02/23/20