Key Concepts: Compositions of Transformations

Definition

A composition of transformations is a combination of two or more transformations applied in sequence. The result of the first transformation is used as the input for the second.

Key Theorems

• Glide Reflection: A translation followed by a reflection over a line parallel to the translation vector.
• Composition of Two Reflections over Parallel Lines = a translation (the distance is twice the distance between the lines).
• Composition of Two Reflections over Intersecting Lines = a rotation about the point of intersection (the angle is twice the angle between the lines).

Properties

• The composition of two isometries is always an isometry.
• Order matters — changing the order of transformations generally changes the result.