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MathidiaMathematics Academy
Transformations and vectors
Lesson 56 of 75
Introduction

Negative enlargements

Objective. Enlarge shapes using negative scale factors.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A negative enlargement scales a shape by a negative scale factor, which both resizes the shape and rotates it 180° about the centre of enlargement, placing the image on the opposite side of the centre from the original. To enlarge a point by a negative scale factor, measure the distance from the centre of enlargement to the point, multiply by the scale factor's size, then place the image that distance away but on the opposite side of the centre. For example, enlarging a point 3 units to the right of the centre by a scale factor of −2 places the image 6 units to the left of the centre. The size of the image is found using the absolute value of the scale factor, while the sign determines the direction flip.

Worked example

A point P is 4 units to the right of the centre of enlargement O. Find the position of the image of P after an enlargement with scale factor −3.

4 … 3
Illustrated card showing 4 … 3
  1. 1The absolute value of the scale factor is 3, so the distance from O becomes 4 × 3 = 12 units.
  2. 2The negative sign means the image is on the opposite side of O from the original point.
  3. 3Since P is to the right of O, the image lies to the left of O.
  4. 4The image is therefore 12 units to the left of O.

Answer: 12 units to the left of O

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Practice

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Common mistake. Pupils often apply the scale factor's size correctly but forget the negative sign means the image appears on the opposite side of the centre, placing it on the same side as the original by mistake. A negative scale factor always flips the image to the opposite side of the centre of enlargement.

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