Knowledge Organiser: Rotations
Key Terms
- Centre of rotation: The fixed point everything rotates around
- Clockwise (CW): Same direction as clock hands
- Anticlockwise (ACW): Opposite to clock hands
- Angle of rotation: How many degrees the shape turns
Must-Know Facts
- Three things to state: centre, angle, direction
- 180° rotation is the same CW or ACW: no need to state direction
- 270° CW = 90° ACW (and vice versa)
- 90° CW about origin: (x, y) → (y, −x)
- 90° ACW about origin: (x, y) → (−y, x)
- 180° about origin: (x, y) → (−x, −y)
Key Methods
- Use tracing paper: trace shape, pin at centre, rotate
- Or apply coordinate formula for rotations about origin
- Rotate each vertex, then join up
- To find centre: perpendicular bisectors of the lines joining each point to its image meet at the centre
Key Formulas
- Rotation 90° clockwise about origin: (x, y) → (y, −x)
- Rotation 90° anticlockwise about origin: (x, y) → (−y, x)
- Rotation 180° about origin: (x, y) → (−x, −y)
- Full description: angle, direction (CW/ACW), centre of rotation
Common Mistakes
- Forgetting direction: Must state clockwise or anticlockwise: 90° CW is different from 90° ACW
- Missing centre of rotation: Always state the centre: "rotation of 90°" is incomplete without it
- Shape changes size: Rotations preserve size and shape: if the image looks different in size, recheck
- 180° rotation = point reflection: A 180° rotation about the origin maps (x, y) to (−x, −y): no need to specify direction