Composing Transformations Worksheet with Answer Key

What's on the worksheet

1. Compose reflections and rotations and name the single motion:
   (r \circ R)(4, 1)(R \circ r)(4, 1)(R \circ s)(-2, 5)(s \circ R)(-2, 5)(t \circ R \circ R)(1, 6)
2. Work out the effect of pressing the Turn and Flip buttons of a drawing app in different orders.
3. Say if each rigid motion keeps or reverses handedness, find its fixed points and name it.
   (x, y) \mapsto (4 - y, x + 2)(x, y) \mapsto (6 - x, y)(x, y) \mapsto (2 - x, -6 - y)(x, y) \mapsto (-2 - x, y - 6)
4. Name the turn or flip, and the translation, in each described motion.
5. Word problem: Hannah's rubber stamp border along a banner.
6. Find where a point lands when a quarter turn and a reflection are done in different orders.