GCSE MATHS • HIGHER TIER
Enlargement Made Simple
Use scale factors and centres of enlargement to resize shapes accurately while preserving similarity.
Clear method
Exam practice
Worked proofs
Enlargement in Four Moves
1
Find the Centre
Identify the fixed centre of enlargement when it is given or required.
2
Identify the Scale Factor
Decide how much larger or smaller the image should become.
3
Scale the Distances
Draw rays through corresponding vertices and multiply distances by the scale factor.
4
Plot and Join
Plot the new vertices accurately and join them to create the enlarged image.
What You’ll Learn
Understand what an enlargement is.
Use positive, fractional and negative scale factors.
Explain why enlargements create similar shapes.
Find image and original dimensions.
Find a scale factor from corresponding lengths.
Understand centres of enlargement.
Perform enlargements accurately on coordinate grids.
Key Rules
Scale factor formula
Image Length = Original Length × Scale Factor
Finding scale factor
Scale Factor = Image Length ÷ Original Length
Centre of enlargement
The centre is the fixed point.
Scale factor size
Greater than 1 = enlargement; between 0 and 1 = reduction.
Worked Proof: Enlargement
Step-by-Step Method
- Identify the centre of enlargement.
- Identify the scale factor.
- Draw rays from the centre through each vertex.
- Multiply each distance from the centre by the scale factor.
- Plot the new vertices accurately.
- Join the new points to complete the enlarged shape.
More Worked Examples
1
Question: A triangle has side length 5 cm and is enlarged by scale factor 3.
5 × 3 = 15
2
Question: A rectangle has length 12 cm and is enlarged by scale factor 1/2.
12 × 1/2 = 6
3
Scale factor = Image ÷ Original
Scale factor = Image ÷ Original
= 3
= 3
Question: Original side length = 4 cm. Enlarged side length = 12 cm. Find the scale factor.
4
Question: A line measures 20 cm and is enlarged by scale factor 0.25.
20 × 0.25 = 5
Answer: 5 cm.
- Common GCSE Mistakes
- Multiplying by the wrong number.
- Forgetting to use the centre of enlargement.
- Confusing enlargement with translation.
- Misunderstanding negative scale factors.
- Forgetting that all lengths change proportionally.
- Exam Tips
- State the scale factor clearly.
- Use the centre of enlargement in grid questions.
- Draw rays through corresponding vertices when locating the centre.
- Remember that fractional scale factors create reductions.
- Treat negative scale factors relative to the centre.
- Check that all corresponding lengths change in the same proportion.
Skills Used in Enlargement
Transformations
Scale Factors
Centres of Enlargement
Similar Shapes
Coordinate Geometry
Ratio and Proportion
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch theEnlargement Tutorial
Step-by-step walkthroughs of Enlargement with clear methods and exam tips.
Frequently Asked Questions
An enlargement changes the size of a shape by multiplying every length by a scale factor.
It creates a larger image.
It creates a reduction.
The image is placed on the opposite side of the centre of enlargement.
It is the fixed point from which the shape grows or shrinks.
All lengths change by the same scale factor, so angles and proportions remain the same.