Sheet № 158 · Foundation + Higher · AQA · Edexcel · OCR
Rotations –
Rotations are one of the four transformations tested in GCSE Maths across AQA, Edexcel, and OCR. A rotation turns a shape around a fixed point called the centre of rotation by a specified angle in a given direction. This guide explains how to perform and describe rotations, covering 90°, 180°, and 270° turns with worked examples from Foun
§Key definitions
Question:
Rotate the triangle with vertices A(1, 2), B(3, 2), and C(3, 4) by 90° clockwise about the origin.
Answer:
The image has vertices A'(2, −1), B'(2, −3), C'(4, −3).
Q1 (Foundation):
Rotate the point (4, 1) by 180° about the origin.
Q2 (Foundation):
Rotate the point (2, 5) by 90° anticlockwise about the origin.
Q3 (Higher):
A shape is rotated so that the point (3, 1) maps to (−1, 3). The centre is the origin. Describe the rotation fully.
§Formulas to memorise
90° clockwise rotation about the origin: (x, y) maps to (y, −x)
90° anticlockwise rotation about the origin: (x, y) maps to (−y, x)
180° rotation about the origin: (x, y) maps to (−x, −y)
Identify the centre of rotation — from the question or diagram.
Use tracing paper. — Trace the shape, place your pencil on the centre of rotation, and turn the tracing paper by the given angle.
Plot the rotated vertices — and draw the image.
To describe a rotation — , find the centre by trial using tracing paper, then state the angle and direction.
Worked example
Rotate the triangle with vertices A(1, 2), B(3, 2), and C(3, 4) by 90° clockwise about the origin. [DIAGRAM: transform | variant=rotate | shape=1,2;3,2;3,4 | cx=0 | cy=0 | angle=-90]
Working:
⚠ Common mistakes
- ✗Not stating all three parts of the description. You must give the centre, the angle, and the direction. Missing any one of these loses marks.
- ✗Confusing clockwise and anticlockwise. Clockwise follows the direction of a clock's hands. If you confuse them, the image ends up in the wrong quadrant.
- ✗Using the wrong centre. If the centre of rotation is not the origin, the coordinate rules above do not apply directly. Use tracing paper instead.
✦ Exam tips
- →Use tracing paper in your exam — it is allowed and makes rotations much easier to perform accurately.
- →For 180° rotations, you do not need to state a direction since both clockwise and anticlockwise produce the same result.
- →A 270° clockwise rotation is the same as a 90° anticlockwise rotation. Use whichever is simpler.
- →When finding the centre of rotation, try the origin first. If that does not work, look for a point equidistant from a vertex and its image.
- →Always check your image by confirming that each image vertex is the same distance from the centre as the corresponding original vertex.