1. Rotations
Coordinate Algebra 5.3

2. Rotations are isometries because they preserve shape and size

3. Rotations on the Coordinate Plane
You can rotate figures clockwise or counterclockwise on the coordinate plane
Counter-
Clockwise
Clockwise

4. Rotating Clockwise!!!!!
0 °
360 °
270 °
90 °
180 °

5. This shows how a triangle can be rotated counter-clockwise about the origin

6. Rules for rotating about the origin (Copy these on your organizer)
0 degrees (x, y) (x, y)
90 deg CW (x, y) (y, -x)
90 deg CCW (x, y) (-y, x)
180 degrees (x, y) (-x,-y)
270 deg CW (x, y) (-y, x)
270 deg CCW (x, y) (y, -x)
360 degrees (x, y) (x, y)
Remember, when you are rotating a figure, rotate each vertex individually, then redraw your figure!

7. That was a lot of rules!! So, to recap:
0, coordinates stay the same
change both signs
90, reverse the order and use coordinate plane to help determine the signs (I will show you what I mean on the next few slides)

8. If You Rotate And You Know It!
If it’s 0 or 360, stay the same
To rotate 180 degrees, change the signs
But if it’s 90 or 270, reverse the order and draw a graph, move the point, and use the signs of the quadrant!

9. Rotating Points About the Origin
(2, 4) 90 ° clockwise
(-3, 6) 180 ° counter-clockwise
(-7, -3) 270 ° clockwise
(5, -4) 90 ° counter-clockwise
(7, -2) 360 ° counter-clockwise

10. Your turn (1, -8) (6, 3) (-3, 4) (3, 1) (-3, -2)
(-1, 8) 180 ° clockwise
(3, -6) 90 ° counter-clockwise
(-4, -3) 270 ° counter- clockwise
(3, 1) 0 °
(-2, 3) 270 ° clockwise
(6, 3)
(-3, 4)
(3, 1)
(-3, -2)

11. Rotating a Figure U (2, 0) V (3, -2) L (-1, -3)

12. Rotating a figure I (-3, 3) N(-2, 3) W(2, 1) D(-1, -1)

13. Writing Rules for the Rotations
Rotation 270 degrees clockwise about the origin OR
Rotation 90 degrees counter clockwise about the origin
Rotation 180 degrees clockwise about the origin OR
Rotation 180 degrees counter clockwise about the origin

14. Rotations Day 2 Mapping figures onto themselves
Rotating about other points

15. Describe the rotations that would map the following regular polygons to itself
To do this, take 360 and divide by the number of sides. Then find the multiples of that number
Pentagon
360/5
72, 144, 216, 288, 360
Octagon
360/8
45, 90, 135, 180, 225, 270, 315, 360
Triangle
360/3
120, 240, 360

17. What would be the difference between rotating this figure about the origin versus rotating about the point (1, -3)?