1. Rotations
EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point?

2. Rotations Center of Rotation: the point you turn the object around
Angle of Rotation: number of degrees to turn the object
Counter clockwise: always turn to the left (unless it says otherwise)

3. On the Coordinate Plane
90° - ONE TURN
180° - TWO TURNS
270° - THREE TURNS

4. 90˚
Center of Rotation
(0, 0)

5. 180˚

6. 270˚

7. Rotating Polygons about their Center
Full circle = 360˚
360÷5
72˚

8. R(2, 5) a) 90° Rotation about the origin

9. R(2, 5) b) 180° Rotation about the origin

10. R(2, 5) c) 270° Rotation about the origin

11. R(-4, 2) a) 90° Rotation about point O

12. R(-4, 2) b) 180° Rotation about point O

13. R(-4, 2) c) 270° Rotation about point O

14. 90˚

15. 180˚

16. 270˚

17. 4.) Point R is the center of regular quadrilateral MATH.
# of sides: ________Degree of each turn: _________
a. 90° rotation of H about R # of turns: _____ Image: ______

18. b. 180° rotation of M about R # of turns: ______ Image: ______
c. 270° rotation of about R # of turns: ________ Image: ________
d. 360° rotation of about R # of turns: _______ Image: _______

19. 5.) Point T is the center of regular decagon ABCDEFGHIJ
# of sides: ______ Degree of each turn: _____
a. 72° rotation of H about T # of turns: _____ Image: _____

20. b. 180° rotation of D about T # of turns: _______ Image: _______
c. 252° rotation of about T # of turns:_______ Image: _______
d. 360° rotation of about R # of turns: _______ Image: ________

21. 6.) Point M is the center of the regular hexagon.
# of sides: ________ Degree of each turn: _________
a. What is the angle of rotation that maps H to X?____

22. b. What is the angle of rotation that maps E to G?______
c. What is the angle of rotation that maps to ?________
d. What is the angle of rotation that maps to ?________

23. Challenge: Perform the following transformations on the figure below.
1. Reflect over the y-axis
2. (x , y) → (x + 1, y – 8)
3. Rotate 270° about the
origin

30. In a coordinate plane, find the
reflection of (2,−4) over the line y = x.           
F (−4,2)
G (4,2)
H (−2,4)
J (4,−2)

31. 70° Rotation
70°

32. 90° Rotation
90°

33. 120° Rotation
120°

34. 180° Rotation
180°

35. 270° Rotation
270°

36. Rules A point (x, y) that has been rotated 90˚ (x, y)→(-y, x)
180˚ (x, y)→(-x, -y)
270° (x, y) → (y, -x)

37. Practice Rotate (1, 5) 90˚ → Rotate (1, 5) 180˚ → Rotate (1, 5) 270˚ →