1 Geometry 4-3 Rotations

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

3 4-3 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 4-3 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 4-3 Rotation 12/7/2017

6 A Rotation is an IsometrySegment lengths do not change. Angle measures do not change. Parallel lines remain parallel. 12/7/2017

7 4-3 Rotation 12/7/2017

8 4-3 Rotation 12/7/2017

9 Rotations on the Coordinate PlaneKnow the formulas for: 90 rotations 180 rotations 270 rotations clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0, 0). 12/7/2017

10 90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2)12/7/2017

11 Rotate (-3, -2) 90 CW Formula (x, y)  (y, x) A’(-2, 3) (-3, -2)12/7/2017

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

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

14 180 clockwise rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2)12/7/2017

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

16 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

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

18 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

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

20 Rotation Formulas 90 CW (x, y)  (y, x) 90 CCW (x, y)  (y, x)180 CW (x, y)  (x, y) 270 CCW (x, y)  (y, x) 12/7/2017

21 Rotational Symmetry A figure can be mapped onto itself by a rotation of 180 or less. 45 90 The square has rotational symmetry of 90. 12/7/2017

22 Does this figure have rotational symmetry?The hexagon has rotational symmetry of 60. 12/7/2017

23 Does this figure have rotational symmetry?Yes, of 180. 12/7/2017

24 Does this figure have rotational symmetry?90 180 270 360 No, it required a full 360 to map onto itself. 12/7/2017

25 Summary A rotation is a transformation where the preimage is rotated about the center of rotation. Rotations are Isometries. A figure has rotational symmetry if it maps onto itself at an angle of rotation of 180 or less. 12/7/2017