Rotation about the origin
A standard method from Coordinates: the steps and worked examples.
Steps
| Rotation | (x, y) becomes |
|---|---|
| 90° anticlockwise | (−y, x) |
| 180° | (−x, −y) |
| 90° clockwise | (y, −x) |
- Sketch the point and decide which quadrant it moves to.
- Apply the rule from the table.
- Check that the answer lies in the quadrant from step 1.
Worked examples
Example 1: Rotation about the origin: rotate (3, −1) through 90° anticlockwise about O.
(3, −1) is in quadrant IV; a quarter-turn anticlockwise takes it to quadrant I
(x, y) → (−y, x)
(3, −1) → (1, 3) quadrant I, as expectedFor the whole topic, read Coordinates: key points, common mistakes and how the DSE tests it.