Turning a shape about a centre, enlarging it from a centre, and finding the angle, centre or scale factor from a diagram.
What you will learn
- Rotate a point or shape by 90° or 180° about a centre
- Enlarge a shape by a whole or fractional scale factor from a centre
- Describe a rotation or an enlargement fully
A rotation is a turn about a centre
A rotation needs three facts: the centre, the angle and the direction (clockwise or anticlockwise).
A half turn, 180°, needs no direction. About the origin the rules are:
90° clockwise: (x, y) → (y, −x)
90° anticlockwise: (x, y) → (−y, x)
180°: (x, y) → (−x, −y)
About any other centre C, work with the vector from C to the point, turn that vector, and add it back on to C.
- Rotate P(5, 3) 90° clockwise about C(2, 1)
- From C to P: 3 across, 2 up
- Turned 90° clockwise: (3, 2) → (2, −3)
- P′ = (2 + 2, 1 − 3) = (4, −2)
To find the centre of a rotation, try points with tracing paper: hold the pencil on a point, turn, and see whether the shape lands on its image. For a half turn, the centre is the midpoint of any point and its image: (−6, −6) and (6, 4) give centre (0, −1).
On a paper, tracing paper is allowed. Trace the shape, hold the centre still with your pencil and turn the paper.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- A rotation is a turn about a centre
- An enlargement multiplies distances from a centre
- The usual slips
- Try it: First question
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Translation, Reflection, Rotation, Enlargement
In this unit: Transformations, congruence and similarity
Translations, reflections, rotations and enlargements on a grid and how to describe them fully, combined transformations and invariant points, the congruence conditions, and similar shapes with their length, area and volume scale factors.