Knowledge Organiser: Rotations
Part of Transformations: Rotations · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Rotations within Transformations: Rotations for GCSE Mathematics. Revise Transformations: Rotations in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 5 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
12 questions
Recall
5 flashcards
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 object→image sides meet at 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
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Read this section alongside the surrounding pages in Transformations: Rotations. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Transformations: Rotations
To fully describe a rotation, which three pieces of information are needed?
Shape A has vertices at (2, 1), (4, 1) and (4, 3). Shape B has vertices at (−1, 2), (−1, 4) and (−3, 4). Fully describe the single transformation that maps shape A onto shape B.
Quick Recall Flashcards
12 questions on Transformations: Rotations — practise free
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