AI Tutor
When you walk along wet sand at the beach, your footprints don't just shift forward β€” each step flips from left foot to right foot while advancing along a line.
This pattern is a composition of transformations, which means applying two or more geometric motions in a specific sequence so that each motion acts on the image of the previous one.
What happens when you combine a flip and a slide along the exact same line?

Glide Reflections

A glide reflection is a special composition that pairs a reflection over a line with a translation running completely parallel to that same line.
Let's track point P(2,5)P(2, 5) through a reflection across the line y=1y = 1 followed by a translation vector ⟨3,0⟩\langle 3, 0 \rangle.
First, P(2,5)P(2, 5) is 4 units above the line y=1y = 1, so reflecting it places Pβ€²P' 4 units below at (2,βˆ’3)(2, -3). Adding the vector ⟨3,0⟩\langle 3, 0 \rangle shifts the xx-coordinate to give the final location Pβ€²β€²(5,βˆ’3)P''(5, -3).
What happens if you place two mirrors parallel to each other and reflect an image twice?

Double Reflections Across Parallel Lines

A double reflection across parallel lines is always equivalent to a single translation in a direction perpendicular to the lines.
The overall translation distance is always twice the distance between the two parallel reflection lines.