1. Composition of Transformations

2. A translation, or glide, and a reflection can be performed one after the other to produce a transformation known as a glide reflection.
Sketch the image of ∆ABC after the glide reflection.
A ( -1,3 ) , B ( -5,-1 ) , C ( -6,-4 )
Translation: ( x , y ) ⇢ ( x + 10 , y)
Reflection : in the x-axis

3. When two or more transformations are combined to produce a single transformation, the result is called a composition of the transformations.
The composition of two (or more) isometries is an isometry.

4. Does the order in which the transformation is performed matter?
Sketch the image of 𝑃𝑄
P ( 2 , -2 ) Q ( 3 , -4 )
Rotation: 90° CCW about the origin
Reflection over the y-axis
Sketch the image of 𝑃𝑄
P ( 2 , -2 ) Q ( 3 , -4 )
Reflection over the y-axis
Rotation: 90° CCW about the origin

5. A ( -1,3 ) , B ( -4,-1 ) , C ( -6,-4 )
Reflection : in the x-axis
Translation: ( x , y ) ⇢ ( x + 10 , y)

6. Guided Practice:
Composition – Problem Solving
Lesson 7.5A
Lesson 7.5B