Positive and fractional enlargements
Scale distances from a centre and distinguish a smaller image from a translation.
Core and Extended.
Before you begin
- Multiply signed values by a fraction.
- Recognise corresponding vertices.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What happens to length for scale factor 1/2?
What you will learn
- Enlarge shapes with positive integer or fractional scale factors.
- Find a scale factor and identify its centre.
Scale the distance from the centre
An enlargement with centre O and scale factor k maps each displacement from O to k times that displacement. For centre (1,1), P(3,5) has displacement (2,4). With k = 1/2, the image displacement is (1,2), so P′ = (2,3). A fractional positive factor makes the shape smaller on the same ray from the centre.
Corresponding side lengths multiply by k, angles stay equal and area multiplies by k². For k = 2, lengths double while area quadruples. The distance between a vertex and its image is not itself the scale factor; use corresponding lengths or centre distances.
Describe the centre as well as the factor
A complete enlargement description names its centre and scale factor. Lines through corresponding vertices meet at the centre, unless the image is unchanged at k = 1, when those data may not identify a unique centre. A vertex at the centre remains fixed during enlargement.
Use a ruler for image edges and place all vertices along the appropriate rays. Core requires positive factors including fractions; negative factors are Extended. An enlargement generally changes size, so it differs from a translation, reflection or rotation even when one vertex happens to stay fixed.
Pause and explain
A shape's area is 12 cm². Enlarge by factor 3. What is the new area?
Worked example
Enlarge P(3,5) by scale factor 1/2 about (1,1).
Show the worked solution
- Displacement from the centre is (2,4).
- Multiply by one half to obtain (1,2).
- Add the centre back: P′ = (2,3).
Answer (2,3).
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Enlarge (2,−3) by factor 2 about the origin.
Give me a hint
Scale the displacement from the origin.
Compare my reasoning
- The displacement is (2,−3).
- Multiply both components by two.
- The image is (4,−6), on the same ray.
(4,−6).
Look for these in your work
- Scaled both coordinates.
- Kept the same direction from the centre.
Enlarge triangle O(0,0), A(6,0), B(0,4) by factor 1/2 about O.
Give me a hint
Halve the centre-to-vertex distances.
Compare my reasoning
- O remains fixed.
- A′ = (3,0), B′ = (0,2).
- The area changes from twelve to three square units.
O′(0,0), A′(3,0), B′(0,2); area 3.
Look for these in your work
- Located all image vertices.
- Squared the length factor for area.
A side of length 5 cm becomes 8 cm under enlargement. Find the factor and image area of an original 25 cm² shape.
Give me a hint
The side-length ratio gives k.
Compare my reasoning
- k = 8/5 = 1.6.
- Area factor is (8/5)² = 64/25.
- New area is 25 × 64/25 = 64 cm².
Factor 1.6; area 64 cm².
Look for these in your work
- Used corresponding lengths.
- Applied the squared factor to area.
Common mistakes
- Multiplying absolute coordinates about a non-origin centre.
- Using k rather than k² for area.
- Describing a smaller image as a translation.
What can you explain now?
What extra detail accompanies an enlargement scale factor?
Compare with the explanation
Its centre.
The centre determines which rays the scaled vertices lie on.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, enlarge one shape about a vertex with factors two and one half.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs 21; Coordinate geometry 10; Geometry 15; Mensuration 13; Trigonometry 13; Transformations and vectors 11; Probability 7; Statistics 13. All 72 syllabus section entries now link to teaching and staged practice. Seven mixed checkpoints sample skills and suggest review lessons. Nine earlier overviews remain available. Full cumulative assessment and human teacher review remain pending. Written lesson practice, charts and constructions are self-checked, not automatically graded. Checkpoints do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources