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

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Presentation transcript:

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.

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

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

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

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

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

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

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”

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

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”

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

P Q Q’ R” R P’ R’ P” Q”

P Q Q’ R” R P’ R’ P” Q”

P Q Q’ R” R P’ R’ P” Q”

P Q’ R” R P’ R’ P” Q” Q

F G F’ G’ F” G”

F G F’ G’ F” G”

G F G’ F’ G” F”

G F G’ F’ G” F”