1. HONORS GEOMETRY 9.3. Rotations

2. Do Now: Complete the do now given to you when you entered class today.

3. Isometries So far we have learned about… Reflections (Mirror/Flip) Translations (Moving in x/y direction) TODAY? Rotations!

4. Rotations: A rotation about a fixed point, called center of rotation, through an angle of x degrees is a function that maps a point to its image such that If the point is the center of rotation then the image and pre-image are the same point If the point is not the center of rotation, then the image and pre- image are the same distance from the center of rotation and the measure of the angle of rotation formed by the pre-image, center of rotation, and image points is x.

5. But first…. 90 degrees CW: 180 degrees CW: 270 degrees CW: 360 degrees CW: 90 degrees CCW: 180 degrees CCW: 270 degrees CCW: 360 degrees CCW: Take Point P (1, 1) Take Point Q (-2, 3)

6. 90 degree rotation To rotate a point 90° counterclockwise about the origin, multiply the y coordinate by -1 and then interchange the x and y coordinates.

7. 180 degree Rotation: To rotate a point 180° counterclockwise about the origin, multiply the x and y coordinates by -1.

8. 270 degree Rotation: To rotate a point 270° counterclockwise about the origin, multiply the x coordinate by -1 and then interchange the x and y coordinates.

9. 360 degree Rotation? What would it look like?

10. So…. To summarize? Angle of RotationCounterclockwise Rotation (LEFT, CCW) Clockwise Rotation (Right CW) 90 Degrees(x, y)  (-y, x)(x, y)  (y, -x) 180 Degrees(x, y)  (-x, -y) 270 Degrees(x, y)  (y, -x)(x, y)  (-y, x)

11. BLARG. Easier Way? Here is what I think about this…. Ask yourself what quadrant is the shape going to end up in…. Then? - If the shape moves Diagonally: Switch the signs - If the shape moves left, right, up or down: Switch the x and y values.

12. Example One: Rotate the shape 90 degrees CCW. What rotation is this equivalent to?

13. Example One (Continued): Rotate the shape 180 degrees CCW. What rotation is this equivalent to?

14. Example One (Continued): Rotate the shape 270 degrees CCW. What rotation is this equivalent to?

15. Example Two: Rotate the shape 90 degrees CW. What rotation is this equivalent to?

16. Example Two (Continued): Rotate the shape 180 degrees CW. What rotation is this equivalent to?

17. Example Two (Continued): Rotate the shape 270 degrees CW. What rotation is this equivalent to?

18. You Try! Rotate the Triangle 180 degrees CCW Rotate the Triangle 270 degrees CW

19. Example Three Rotate the following 90 degrees CW

20. Example Three (Continued) Rotate the following 180 degrees CW

21. Example Four: Rotate the shape 90 degrees CCW

22. Example Four (Continued): Rotate the shape 180 degrees CCW

23. You Try! Rotate the following image 90 degrees CW, and 180 degrees CCW.

24. Practice Problems Try some on your own/in small groups As always don’t hesitate to ask me questions if you are confused/talk to your table mates! They are your greatest resource!

25. Exit Ticket: If we rotate the shape 90 degrees CW, where does point A and D end up? If we rotate the shape 180 degrees CCW, where does point A and D end up?