Sheet № 220 · Higher only · AQA · Edexcel · OCR
Negative Scale Factor Enlargement –
Negative scale factor enlargement is a Higher-tier GCSE Maths topic tested on AQA, Edexcel, and OCR papers. A negative scale factor produces an image that is inverted (upside down and flipped left-to-right) and appears on the opposite side of the centre of enlargement. This guide explains the concept, shows you how to draw negative enlarg
§Key definitions
Question:
Triangle A has vertices at (2, 1), (4, 1), and (2, 3). Enlarge it by scale factor −1 about the origin (0, 0).
Answer:
The image vertices are (−2, −1), (−4, −1), and (−2, −3).
Q1 (Higher):
A square has vertices at (2, 2), (4, 2), (4, 4), and (2, 4). Enlarge by scale factor −1 about (3, 3). What are the image coordinates?
Q2 (Higher):
Triangle C at (0, 0), (4, 0), (0, 3) is enlarged by SF = −½ about (0, 0). Find the image.
Q3 (Higher):
An enlargement maps point (2, 3) to (−4, −3) with centre (0, 1). Find the scale factor.
§Formulas to memorise
For each point, draw a line from the centre through the point. Multiply the distance by the scale factor. A negative value means measure in the opposite direction.
|SF| = 1: the image is the same size (but inverted for negative).
Worked example
Triangle A has vertices at (2, 1), (4, 1), and (2, 3). Enlarge it by scale factor −1 about the origin (0, 0).
This topic is Higher only, but this example uses simple coordinates.
⚠ Common mistakes
- ✗Forgetting to go through the centre to the other side. With a negative scale factor, the image point is on the opposite side of the centre from the original — not on the same side.
- ✗Ignoring the negative sign when calculating size. The image size depends on |SF|. A scale factor of −2 means the image is twice as large, not smaller.
- ✗Describing the transformation without all three details. You must state: (1) enlargement, (2) scale factor (including sign), and (3) centre of enlargement to earn full marks.
✦ Exam tips
- →Use the vector method: find the vector from the centre to each vertex, multiply by the scale factor, then add back to the centre. This avoids mistakes with direction.
- →If a question shows the original and image on opposite sides of a point, suspect a negative scale factor.
- →The image is always similar to the original (same angles, proportional sides). Negative SF also inverts orientation.
- →On coordinate grids, count squares carefully to find the centre — it lies on the line joining each original vertex to its image.