1. Rotations Geometry Unit 7, Lesson 3 Mrs. King

2. What is a Rotation? Definition: A turn. Example?

3. London Eye

4. Directions of Rotations! Positive rotations go in a counterclockwise direction. Negative rotations go in a clockwise direction. Clockwise Counterclockwise Illustration from: http://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htm

5. Rotation Rule 90°: (x,y)  (-y,x) Swap the numbers and change the new “x” value sign.

6. Rotation Rule 90°: 180°: 270°: 360°: (x,y)  (-y,x) Rotate 90° two times Rotate 90° three times NOTHING!

7. Graphing Coordinates Rotate the point (4,7): –90°: –180°: –270°: –360°: y x 10 -10 (-7,4) (-4,-7) (7,-4) (4,7) (-7,4) (-4,-7) (7,-4)

8. Example 1: Graph the vertices of parallelogram WXYZ. –W(-7,1) –X(-3,1) –Y(-2,5) –Z(-6,5) Rotate the parallelogram 90°. y x 10 -10 WX Y Z W’(-1,-7) X’(-1,-3) Y’(-5,-2) Z’(-5,-6) W’ X’ Y' Z’

9. Example 2: Graph the vertices of parallelogram WXYZ. –W(-7,1) –X(-3,1) –Y(-2,5) –Z(-6,5) Rotate the parallelogram 270°. y x 10 -10 WX Y Z W’(1,7) X’(1,3) Y’(5,2) Z’(5,6) W’ X’ Y' Z’ (-1,-7)(7,-1)

10. Practice with Rotations http://www.regentsprep.org/Regents/ma th/geometry/GT4/PracRot.htm http://www.regentsprep.org/Regents/ma th/geometry/GT4/PracRot.htm

11. Practice: A(2,3), B(2,-1), C(-1,-1) Graph triangle ABC under the following rotations:

12. Answer: