Geometric Transformations

Translation (slide): (x, y) to (x + a, y + b) Reflection: - Over x-axis: (x, y) to (x, -y) - Over y-axis: (x, y) to (-x, y) - Over y = x: (x, y) to (y, x) Rotation about the origin: - 90° counterclockwise: (x, y) to (-y, x) - 180°: (x, y) to (-x, -y) - 270° counterclockwise (or 90° clockwise): (x, y) to (y, -x) Dilation with scale factor k from origin: (x, y) to (kx, ky)

Example: Reflect (3, -5) over the y-axis, then translate by (2, 1).

Memorize the reflection rules. The ACT's favorite: reflection over the x-axis (negate y) and over the y-axis (negate x). For 180° rotation, just negate both coordinates.