1. 7.5 Composition Transformations California Standards for Geometry 17: Prove theorems using coordinate geometry 22: Know the effect of rigid motions on figures in the coordinate plane.

2. Definition Composition Transformations Two or more transformations combined to produce a single transformation.

3. Definition Composition Transformations Two or more transformations combined to produce a single transformation.

4. Definition Composition Transformations Two or more transformations combined to produce a single transformation.

5. P” Q” P” Q” P’ Q’ Definition Glide reflection a composition transformation that first is a translation mapping P onto P ’ and then is a reflection in a line parallel to the direction of the translation that maps P ’ onto P ”. P Q

6. Sketch the image of  QRS after a glide reflection Translation: Reflection: in the y -axis Q R S Q’ R’ S’ Q” R” S”

7. Composition Transformations The commutative property does not necessarily work with composition transformations (order matters)

8. Sketch the image of after the following composition: Reflection: in the x -axis Rotation: 270 o counterclockwise about the origin C D D’ C’ 270 o C”

9. C D D’ C’ 270 o D” C” Sketch the image of after the following composition: Reflection: in the x -axis Rotation: 270 o counterclockwise about the origin

10. Sketch the image of quad ABCD after the following composition: Reflection: in the line x = 1 Rotation: 90 o clockwise about (1, 0) A B D’ C’ D” C” D C A’ B’ A” B”

11. Composition Transformations Composition Theorem –The composition of two (or more) isometries is an iosmetry.

12. P Q Q’ R” R P’ R’ P” Q”

13. P Q Q’ R” R P’ R’ P” Q”

14. P Q Q’ R” R P’ R’ P” Q”

15. P Q’ R” R P’ R’ P” Q” Q

16. F G F’ G’ F” G”

17. F G F’ G’ F” G”

18. G F G’ F’ G” F”

19. G F G’ F’ G” F”