Rotations
Grade 5Describing a rotation
To describe a rotation fully, you need three things: the angle, the direction (clockwise or anticlockwise), and the centre of rotation. Miss any one of these and the description is incomplete.
Note: 180° is the same clockwise or anticlockwise, so direction is not needed for a half-turn.
The coordinate rules for rotations about the origin
90° anticlockwise: (x, y) → (−y, x). 90° clockwise: (x, y) → (y, −x). 180°: (x, y) → (−x, −y).
If you cannot remember the rules, trace the point on a sketch grid and rotate physically. For 90° anticlockwise, think "the x becomes the new y, and the y becomes the new negative x".
Worked example
EXAMPLE
Rotate point P(4, 1) by 90° clockwise about the origin.
90° clockwise: (x, y) → (y, −x). P(4, 1) → (1, −4). Answer: (1, −4).
Finding the centre
To find the centre of rotation, draw perpendicular bisectors of lines joining corresponding points on the object and image. Where they meet is the centre of rotation.
