Math Playground
Geometry

Rotation

Spin around a point — every distance from that point is preserved.

Rotation spins a shape around a fixed point — the centre of rotation — by an angle, clockwise or anticlockwise. Like a hand sweeping around a clock face.

Turn the shape
Turn: 90°
original image

The three things a rotation needs

  • A centre — the pivot point. It's the only point that stays still.
  • An angle — how far to turn (90°, 180°, 45°…).
  • A direction — clockwise or anticlockwise (anticlockwise is the positive direction in maths).
  • Everything else: lengths, angles, area and orientation are all preserved — the image is congruent and *not* mirrored.
Your turn

Rotate the point (4, 0) by 90° anticlockwise about the origin. Where is it now?

Two reflections in intersecting lines = one rotation about the crossing point, through twice the angle between the lines. Spin the slider above to 360° and the image lands exactly back on the original.