Rotation in Geometry
What is a Rotation?
A rotation is a transformation that turns a figure about a fixed point called the center of rotation. Every point of the figure moves along a circular arc centered at that point.
A rotation is defined by three things:
- 1. Center of Rotation — the fixed point around which the figure turns
- 2. Angle of Rotation — how far the figure turns (measured in degrees)
- 3. Direction — counterclockwise (positive) or clockwise (negative)
Key Properties of Rotation
Rotation is a Rigid Transformation (Isometry)
- Distances are preserved
- Angle measures are preserved
- The image is congruent to the pre-image
- Orientation (order of vertices) is preserved
Convention
- Counterclockwise (CCW) = positive angle
- Clockwise (CW) = negative angle
- A full rotation = $360°$
- A half rotation = $180°$
- A quarter rotation = $90°$