Rotation by 90° about the origin
90° anticlockwise sends (x,y) to (−y,x); clockwise sends (x,y) to (y,−x).
Key formulas
One vertex test
Start with a single easy point such as (2,0). Anticlockwise 90° should land on (0,2).
Whole shape
Apply the same rule to every vertex. Distances from the origin stay constant.
Example
Triangle (1,1),(4,1),(1,3) → anticlockwise (−1,1),(−1,4),(−3,1).
Worked example
Worked example
Problem. Rotate the point (3, −2) by 90° anticlockwise about the origin.
Solution. (x, y) → (−y, x) so (3, −2) → (2, 3).
180°
180° about O is (x,y)→(−x,−y).
Review quiz
90° clockwise about O sends (5,0) to:
Practice questions
- Rotate (3,−2) by 90° anticlockwise about O.
- Rotate (5,0) by 90° clockwise about O.
Study notes
About another centre?
Translate so the centre goes to O, rotate, then translate back.