Rotations

Description

A rotation turns a shape around a fixed point called the centre of rotation. To describe a rotation fully, give:

1. The centre of rotation (as a coordinate)
2. The angle of rotation
3. The direction — clockwise or anticlockwise

$$90° \text{ clockwise} = 270° \text{ anticlockwise}$$

Tracing paper method: place tracing paper over the shape, trace it, put your pencil on the centre, rotate the paper by the required angle, then mark the new position.

Rotating a point: for a 90° anticlockwise rotation about the origin, $(x, y) \to (-y, x)$. For 180°: $(x, y) \to (-x, -y)$.

The object and image are congruent — the shape does not change size. Rotations, like reflections and translations, are isometries (they preserve length and angle).

Common error: rotating in the wrong direction (clockwise vs anticlockwise), or measuring the angle from the wrong line.

Links

Coordinates Translations Reflections