Translations, rotations & reflections

Move a shape while keeping track of every vertex.

The idea

Translation adds the same displacement to every point. Reflection reverses one coordinate across a coordinate axis: (x, −y) across the x-axis and (−x, y) across the y-axis. A 90° counterclockwise rotation about the origin sends (x, y) to (−y, x). These transformations preserve distances and angles.

Work through an example

Reflect A(−2, −1) across the x-axis to get A′(−2, 1). Rotating the original A by 90° counterclockwise gives A′(1, −2). Translating the original by (3, 2) gives A′(1, 1).

What to watch for

The center of rotation matters. Our playground rotates around the origin. Positive angles turn counterclockwise; changing the order of different transformations can change the final result.