Key Concepts: Rotations

Definition

A rotation turns a figure around a fixed point called the center of rotation by a given angle.

Coordinate Rules (about the origin)

• 90° counterclockwise: (x, y) → (−y, x)
• 180°: (x, y) → (−x, −y)
• 270° counterclockwise (or 90° clockwise): (x, y) → (y, −x)

Properties of Rotations

• A rotation is an isometry (preserves distances and angle measures).
• Orientation is preserved.
• The center of rotation is the only point that does not move.