7.5 Composition Transformations

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

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

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

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

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

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