A transformation changes the position, orientation or size of a shape using a precise rule. A translation slides every point by the same vector; a reflection flips a shape across a mirror line; a rotation turns it about a centre. An enlargement multiplies distances from a centre by a scale factor. Congruent shapes have matching lengths and angles, so they are the same size and shape even if their orientation differs. Similar shapes have matching angles and proportional corresponding lengths. Use labels to match the correct sides rather than simply pairing the left sides of two diagrams.
Learning objectives
- Describe and perform a transformation completely.
- Distinguish similarity from congruence.
Key ideas
A translation specifies horizontal and vertical movements, often as a column vector.
A reflection needs a mirror line; a rotation needs a centre, angle and direction.
An enlargement needs a centre and scale factor. For a positive factor, multiply distances from the centre.
Similar figures have equal corresponding angles and a common corresponding length ratio.
Congruent figures have equal corresponding lengths and angles. Use a valid triangle congruence test.
Worked examples
Example 1
Enlarge the point about the origin by the given positive factor.
Multiply both distances from the origin.
Answer
Example 2
Reflect the point in the vertical axis.
Reverse the horizontal coordinate; keep the vertical coordinate.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Describe or carry out a reflection, rotation, translation or enlargement.
AO2 · Reasoning
Give all the information needed to describe a transformation uniquely.
AO3 · Problem solving
Use similarity to find an inaccessible length or connect two diagrams.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Equal corresponding angles establish triangle similarity, not congruence. An enlargement acts on distances from its centre.
Try it yourself
Attempt each question before opening its answer.
Check 1: Reflect the point (3, -2) in the y-axis.
Answer: (-3, -2)
Reflection in the y-axis reverses the horizontal coordinate while keeping the vertical coordinate.
Check 2: Two similar triangles have corresponding sides 6 cm and 9 cm. The smaller triangle has another side 8 cm. Find the matching larger side.
Answer: 12 cm
The scale factor from smaller to larger is 9/6 = 1.5. The matching side is 8 × 1.5 = 12 cm.
Explain it in your own words
- Describe all details needed for each of the four transformations.
- Draw a reflection and mark equal perpendicular distances from the mirror line.
- Explain why equal angles prove triangle similarity but do not guarantee the same size.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Geometry specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.