Transformations Rotations on a Coordinate Plane Meet TED

Transformations: Rotations on a Coordinate Plane Meet TED is going to help us learn about rotations. First let’s focus on TED’s 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

Rotations on the Coordinate Plane Know the formulas for: • 90 rotations • 180 rotations • clockwise & counterclockwise Unless told otherwise, the center of rotation is the origin (0, 0). 10/28/2020

90 clockwise rotation A(-2, 4) Formula (x, y) (y, x) A’(4, 2) 10/28/2020

Rotate (-3, -2) 90 clockwise Formula A’(-2, 3) (-3, -2) 10/28/2020 (x, y) (y, x)

90 counter-clockwise rotation Formula A’(2, 4) (x, y) ( y, x) A(4, -2) 10/28/2020

Rotate (-5, 3) 90 counter-clockwise Formula (-5, 3) (-3, -5) 10/28/2020 (x, y) ( y, x)

180 rotation Formula (x, y) ( x, y) A’(4, 2) A(-4, -2) 10/28/2020

Rotate (3, -4) 180 Formula (-3, 4) (x, y) ( x, y) (3, -4) 10/28/2020

Rotation Example Draw a coordinate grid and graph: B(-2, 4) A(-3, 0) 10/28/2020 C(1, -1) Draw ABC

Rotation Example B(-2, 4) Rotate ABC 90 clockwise. A(-3, 0) 10/28/2020 Formula C(1, -1) (x, y) (y, x)

Rotate ABC 90 clockwise. B(-2, 4) A’ B’ A(-3, 0) C’ C(1, -1) 10/28/2020 (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) 10/28/2020 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) 10/28/2020

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’ 10/28/2020 A’ B(-2, 4) B’(-4, -2) C(1, -1) C’(1, 1)

Rotation Formulas n n n 90 CW 90 CCW 180 10/28/2020 (x, y) (y, x) (x, y) ( y, x) (x, y) ( x, y)

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