1. The distance from the center to any point on the shape stays the same.
Rotations
A turn around a center.
The distance from the center to any point on the shape stays the same.

2. Rotations  degrees & direction
Clockwise

3. 𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙)
A rotation turns a figure through an angle about a fixed point called the center.  It is a rigid isometry.
Rules of rotation are for clockwise rotations.
Rotation of 90°:
   
Rotation of 180°:   
Rotation of 270°:
    
𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙)
𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚)
𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙)
Counter clockwise rotations are opposite clockwise.
90°cw = 270°ccw and 270°cw = 90°ccw

4. Rotate ∆TSN 90°cw (x, y)  (y, -x)
T(-1, 1)  T'(1, 1)
S(4, -1)  S'(-1, -4)
N(1, -4)  N'(-4, -1) N’ S’
(270 ° CCW rotation)

5. T(-1, 1)  T'(1, -1) S(4, -1)  S'(-4, 1) N(1, -4)  N'(-1, 4)
Rotate ∆TSN 180°
(x, y)  (-x, -y)
T(-1, 1)  T'(1, -1) S(4, -1)  S'(-4, 1) N(1, -4)  N'(-1, 4)

6. T(-1, 1)  T'(-1, -1) S(4, -1)  S'(1, 4) N(1, -4)  N'(4, 1)
Rotate ∆TSN 270° cw
(x, y) to (-y, x)
T(-1, 1)  T'(-1, -1) S(4, -1)  S'(1, 4) N(1, -4)  N'(4, 1)

7. Rotate 90 CW about the Origin (Same as 270 CCW)
Change the sign of x and switch the order

9. Rotate 90 CW

11. Rotate 270 Clockwise (Same as 90 ccw)
Change the sign of y and switch the order

12. Rotate 90° counterclockwise about the origin

13. Rotate 90° counterclockwise about the origin

14. Rotate 180 about the Origin
ONLY Change the signs

15. Rotate 180° about the origin

16. Rotate 180° about the origin

17. 𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙)
A rotation turns a figure through an angle about a fixed point called the center.  It is a rigid isometry.
Rules of rotation are for clockwise rotations.
Rotation of 90°:
   
Rotation of 180°:   
Rotation of 270°:
    
𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙)
𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚)
𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙)
Counter clockwise rotations are opposite clockwise.
90°cw = 270°ccw and 270°cw = 90°ccw

18. Virtual Nerd Tutoring Lessons
Lesson on Rotations
Lesson on Rotations 90°
Lesson on Rotations 180°

19. Coordinate Rules for Rotations about the origin: When a point (x, y) is rotated clockwise about the origin, the following rules are true:
For a rotation of 900(x, y)  (y, -x).
For a rotation of 1800 (x,y)  (-x, -y).
For a rotation of 2700 (x,y)  (-y, x).
When a point (x, y) is rotated counterclockwise about the origin, the following rules are true:
For a rotation of 900 (x,y)  (-y, x).
For a rotation of 2700 (x, y)  (y, -x).