1. ROTATION

2. 12/7/2015 Goals Identify rotations in the plane. Apply rotation to figures on the coordinate plane.

3. 12/7/2015 Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation

4. The center of rotation could be a point outside the shape or on the shape A ROTATION MEANS TO TURN A FIGURE center of rotation

5. ROTATION A ROTATION MEANS TO TURN A FIGURE The triangle was rotated around the point. center of rotation

6. ROTATION If a shape spins 360 , how far does it spin? 360 

7. ROTATION If a shape spins 180 , how far does it spin? 180  Rotating a shape 180  turns a shape upside down.

8. ROTATION If a shape spins 90 , how far does it spin? 90 

9. ROTATION Describe how the triangle A was transformed to make triangle B AB Describe the translation. Triangle A was rotated right 90 

10. ROTATION Describe how the arrow A was transformed to make arrow B Describe the translation. Arrow A was rotated right 180  A B

11. 12/7/2015 Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. Center of Rotation 90  G G’

12. 12/7/2015 A Rotation is an Isometry (Rigid Transformation) Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged.

13. 12/7/2015 Rotations on the Coordinate Plane Be able to do: 90  rotations 180  rotations clockwise & counter- clockwise Unless told otherwise, the center of rotation is the origin (0, 0).

14. 12/7/2015 90  clockwise rotation Formula (x, y)  (y,  x) A(-2, 4) A’(4, 2) Or… Use the relation between the slopes of two perpendicular lines

15. 12/7/2015 Rotate (-3, -2) 90  clockwise Formula (x, y)  (y,  x) (-3, -2) A’(-2, 3) Or… Use the relation between the slopes of two perpendicular lines

16. 12/7/2015 90  counter-clockwise rotation Formula (x, y)  (  y, x) A(4, -2) A’(2, 4)

17. 12/7/2015 Rotate (-5, 3) 90  counter-clockwise Formula (x, y)  (  y, x) (-3, -5) (-5, 3)

18. 12/7/2015 180  rotation Formula (x, y)  (  x,  y) A(-4, -2) A’(4, 2)

19. 12/7/2015 Rotate (3, -4) 180  Formula (x, y)  (  x,  y) (3, -4) (-3, 4)

20. 12/7/2015 Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw  ABC A(-3, 0) B(-2, 4) C(1, -1)

21. 12/7/2015 Rotation Example Rotate  ABC 90  clockwise. Formula (x, y)  (y,  x) A(-3, 0) B(-2, 4) C(1, -1)

22. 12/7/2015 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(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

23. 12/7/2015 Rotate  ABC 90  clockwise. Check by rotating  ABC 90 . A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’

24. 12/7/2015 Rotation Formulas 90  CW(x, y)  (y,  x) 90  CCW(x, y)  (  y, x) 180  (x, y)  (  x,  y) These rules only work when the center of rotation is the origin. Use the opposite reciprocal relation between the slopes of perpendicular lines to do rotations about other points.

25. 12/7/2015 Rotating segments A B C D E F G H O

26. 12/7/2015 Rotating AC 90  CW about the origin maps it to _______. A B C D E F G H CE O

27. 12/7/2015 Rotating HG 90  CCW about the origin maps it to _______. A B C D E F G H FE O

28. 12/7/2015 Rotating AH 180  about the origin maps it to _______. A B C D E F G H ED O

29. 12/7/2015 Rotating GF 90  CCW about point G maps it to _______. A B C D E F G H GH O

30. 12/7/2015 Rotating ACEG 180  about the origin maps it to _______. A B C D E F G H EGAC AE C G O

31. 12/7/2015 Rotating  FED 270  CCW about point D maps it to _______. A B C D E F G H  BOD O

32. 12/7/2015 Summary A rotation is a transformation where the preimage is rotated about the center of rotation. Rotations are Rigid Transformations

33. 12/7/2015

34. Homework