Composition of Transformations

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Presentation transcript:

Composition of Transformations

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

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.

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

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

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