1 Geometry Rotations

2 Goals Identify rotations in the plane.Apply rotation formulas to figures on the coordinate plane. 12/7/2017

3 Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation 12/7/2017

4 Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. G 90 Center of Rotation G’ 12/7/2017

5 A Rotation is an IsometrySegment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged. 12/7/2017

6 Rotations on the Coordinate PlaneKnow the formulas for: 90 rotations 180 rotations clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0, 0). 12/7/2017

7 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2)12/7/2017

8 Rotate (-3, -2) 90 clockwiseFormula (x, y)  (y, x) A’(-2, 3) (-3, -2) 12/7/2017

9 90 counter-clockwise rotationFormula (x, y)  (y, x) A’(2, 4) A(4, -2) 12/7/2017

10 Rotate (-5, 3) 90 counter-clockwiseFormula (x, y)  (y, x) (-5, 3) (-3, -5) 12/7/2017

11 180 rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2) 12/7/2017

12 Rotate (3, -4) 180 Formula (x, y)  (x, y) (-3, 4) (3, -4)12/7/2017

13 Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4)Draw ABC A(-3, 0) C(1, -1) 12/7/2017

14 Rotation Example Rotate ABC 90 clockwise. Formula (x, y)  (y, x)12/7/2017

15 Rotate ABC 90 clockwise.(x, y)  (y, x) A(-3, 0)  A’(0, 3) B(-2, 4)  B’(4, 2) C(1, -1)  C’(-1, -1) A’ B’ A(-3, 0) C’ C(1, -1) 12/7/2017

16 Rotate ABC 90 clockwise.Check by rotating ABC 90. A’ B’ A(-3, 0) C’ C(1, -1) 12/7/2017

17 Rotation Formulas 90 CW (x, y)  (y, x) 90 CCW (x, y)  (y, x)180 (x, y)  (x, y) Rotating through an angle other than 90 or 180 requires much more complicated math. 12/7/2017