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MathidiaMathematics Academy
Transformations and vectors
Lesson 57 of 75
Easy practice

Fractional enlargements

Objective. Enlarge shapes using fractional scale factors.

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

Learn: the key idea

A fractional enlargement uses a scale factor between 0 and 1, which makes the resulting image smaller than the original shape while keeping it similar, with all distances from the centre of enlargement multiplied by that fraction. To enlarge a point by a fractional scale factor, measure the distance from the centre to the point, multiply by the fraction, and place the image that new, shorter distance away in the same direction as the original. For example, enlarging a point 12 units from the centre by a scale factor of 1/3 places the image just 4 units from the centre, in the same direction. Despite 'enlargement' being in the name, fractional scale factors between 0 and 1 actually shrink the shape.

Worked example

A point Q is 15 units from the centre of enlargement O. Find the distance of its image from O after an enlargement with scale factor 1/5.

1/5
Fraction bar showing 1 out of 5 parts shaded
  1. 1The scale factor is 1/5, which is between 0 and 1, so the image will be smaller.
  2. 2Multiply the original distance by the scale factor: 15 × 1/5.
  3. 315 × 1/5 = 3.
  4. 4The image is 3 units from O, in the same direction as the original point.

Answer: 3 units from O

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Practice

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Common mistake. Pupils often assume 'enlargement' always means a bigger shape, mistakenly multiplying the original size when a fractional scale factor less than 1 should shrink it instead. Remember that a scale factor between 0 and 1 always makes the image smaller.

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