GCSE Maths Transformations Notes
A transformation changes a shape's position or size. The four you need are translation, reflection, rotation and enlargement.
Key concepts
- Translation
- A slide described by a column vector giving movement across and up/down.
- Reflection
- A mirror image in a given line, e.g. y = x or the x-axis.
- Rotation
- A turn about a centre by an angle and direction (clockwise or anticlockwise).
- Enlargement
- A change of size by a scale factor from a centre of enlargement.
Key formulas
Translation vector
( x across, y up )
Enlargement
new length = scale factor × original length
Worked example
Describe fully the single transformation that maps shape A onto a shape twice as large from the origin.
- 1The shape changes size, so it is an enlargement.
- 2It is twice as large, so the scale factor is 2.
- 3State the centre of enlargement: the origin (0, 0).
Answer: Enlargement, scale factor 2, centre (0, 0)
Common mistakes
✗ Giving only part of the description.
✓ State every detail — e.g. rotation needs angle, direction and centre.
✗ Mixing up the order in a translation vector.
✓ Top number is across (x), bottom number is up/down (y).
✗ Describing two transformations when one is asked for.
✓ If a question says 'single transformation', give exactly one.
Quick check
Try these, then reveal the answers.
Which transformation changes size?Reveal answer
Enlargement.
What describes a translation?Reveal answer
A column vector.
What three things describe a rotation?Reveal answer
Angle, direction and centre.
Exam tips
- Use tracing paper for rotations to check the turn.
- For 'describe fully', include every required detail to score full marks.
- A negative scale factor enlargement turns the shape upside down through the centre.
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Frequently asked questions
How do I describe a rotation fully?+
Give the angle, the direction (clockwise or anticlockwise) and the centre of rotation.
What information describes an enlargement?+
The scale factor and the centre of enlargement.
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