Sheet № 160 · Foundation + Higher · AQA · Edexcel · OCR
Enlargement and Centre of Enlargement –
Enlargement is the transformation that changes the size of a shape while keeping it the same proportions. It is the only transformation that does not preserve congruence. Enlargement questions appear on both Foundation and Higher GCSE Maths papers, with fractional and negative scale factors reserved for Higher. This guide covers integer,
§Key definitions
Question:
Enlarge the triangle with vertices A(1, 1), B(3, 1), and C(1, 3) by scale factor 2 from the centre (0, 0).
Answer:
The image has vertices A'(2, 2), B'(6, 2), C'(2, 6).
Q1 (Foundation):
Enlarge the point (2, 3) by scale factor 3 from the origin.
Q2 (Foundation):
A shape is enlarged so that a side of 4 cm on the object becomes 10 cm on the image. What is the scale factor?
Q3 (Higher):
Enlarge the point (5, 3) by scale factor −2 from the centre (1, 1). Find the image coordinates.
§Formulas to memorise
Image distance from centre = scale factor × object distance from centre
Scale factor = image length ÷ object length
Identify the centre of enlargement — and the scale factor from the question.
For each vertex — , draw a ray from the centre through the vertex.
Measure the distance — from the centre to the vertex and multiply by the scale factor.
Plot the image vertex — at the new distance along the same ray (or the opposite direction for negative scale factors).
Join the image vertices — to complete the enlarged shape.
Worked example
Enlarge the triangle with vertices A(1, 1), B(3, 1), and C(1, 3) by scale factor 2 from the centre (0, 0).
Working:
⚠ Common mistakes
- ✗Forgetting to use the centre of enlargement. Multiplying the coordinates by the scale factor only works when the centre is (0, 0). For any other centre, use vectors from the centre first.
- ✗Drawing rays in the wrong direction for negative scale factors. A negative scale factor means the image is on the opposite side of the centre. The ray goes through the centre and out the other side.
- ✗Incomplete description. To describe an enlargement fully, state the transformation type (enlargement), the scale factor, and the centre. All three are required.
✦ Exam tips
- →When finding the centre of enlargement, draw rays from corresponding vertices of the object and image back until they meet. The intersection is the centre.
- →A scale factor of −1 produces a shape the same size on the opposite side of the centre — this is equivalent to a 180° rotation about that point.
- →Check your answer by verifying that corresponding sides of the image are in the correct ratio to the original.
- →On Higher papers, expect questions combining fractional or negative scale factors with finding the centre.