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

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 opposite direction of a clock (unless told 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 about a Center Point
Full circle = 360˚
360÷5
72˚

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

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

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

11. R(4, 3) 90° rotation about point (2, 2)

12. R(4, 3) 180° rotation about point (2, 2)

13. R(4, 3) 270° rotation about point (2, 2)

14. 90° rotation about the origin

15. 270° rotation about the origin

16. 180° rotation about the point (-4, 2)

17. Ex 3) Point R is the center of regular quadrilateral MATH.
# of sides: ________
Degree of each turn: _________

18. a. 90° rotation of H about R # of turns: _____ Image: ______
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. You Try! Point T is the center of regular decagon ABCDEFGHIJ
# of sides: ______
Degree of each turn: _____

20. a. 72° rotation of H about T # of turns: _____Image: _____
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. Ex 4) Point M is the center of the regular hexagon.
# of sides: ________
Degree of each turn: _________

22. a. What is the angle of rotation that maps H to X?____
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. You Try!
Determine 3 angles of rotation that would map a regular octagon back onto itself.

24. Point Symmetry?

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

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

33. 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)