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Enlargements

FoundationHigherAQAEdexcelOCR

Enlargements is a key geometry topic at GCSE Maths. This Foundation and Higher worksheet gives you exam-style questions on enlarging shapes by a scale factor, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Multiply each distance from the centre by the scale factor.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

An enlargement changes the size of a shape by a scale factor, measured from a fixed point called the centre of enlargement.

A scale factor greater than \(1\) makes the shape larger, and a fraction between \(0\) and \(1\) makes it smaller — though it is still called an enlargement. A negative scale factor produces an image on the opposite side of the centre, turned upside down.

A full description needs both the scale factor and the centre. The lengths change by the scale factor, but the angles stay the same, which is why the object and image are similar rather than congruent.

Revision notes

Performing an enlargement

Measure from the centre to each vertex, multiply that distance by the scale factor, and mark the new point along the same line.

Drawing rays from the centre through each vertex makes the construction accurate and shows the method.

Fractional and negative scale factors

A scale factor between \(0\) and \(1\) makes the image smaller.

A negative scale factor puts the image on the opposite side of the centre and inverts it. So a scale factor of \(-2\) doubles the size and rotates it by \(180^\circ\).

Finding the centre and scale factor

The scale factor is the ratio of a length on the image to the matching length on the object.

The centre is found by drawing lines through matching vertices and extending them until they meet.

Key points

  • An enlargement changes size by a scale factor.
  • It needs a centre of enlargement.
  • A scale factor over 1 makes the shape larger.
  • A fractional scale factor makes it smaller.
  • A negative scale factor inverts the image.
  • Angles stay the same, so the shapes are similar.

Worked examples

Example 1

A shape is enlarged by scale factor \(3\). A side of \(4\)cm becomes what length?

Working

\[4 \times 3\]multiply the length by the scale factor
\[= 12\text{cm}\]state the new length

Example 2

A side of \(10\)cm becomes \(4\)cm. Find the scale factor.

Working

\[\frac{4}{10}\]divide the image length by the object length
\[= 0.4\]the shape gets smaller

Example 3

State the two things needed to describe an enlargement fully.

Working

\[\text{The scale factor}\]how much the size changes
\[\text{The centre of enlargement}\]the fixed point it is measured from

Common mistakes

  • Forgetting the centre of enlargement.

    A description needs both the scale factor and the centre.

  • Thinking a fractional scale factor is a reduction, not an enlargement.

    It is still called an enlargement even though the shape gets smaller.

  • Changing the angles.

    Only lengths change; angles stay the same.

  • Measuring from the wrong point.

    All distances are measured from the centre of enlargement.

Exam tips

  • Draw rays from the centre through each vertex.
  • Give both the scale factor and the centre in a description.
  • Check the angles are unchanged.
  • Remember a fractional scale factor still counts as an enlargement.

Key terms

Enlargement
A transformation changing size by a scale factor.
Scale factor
The multiplier applied to each length.
Centre of enlargement
The fixed point distances are measured from.
Similar
Same shape, different size, with equal angles.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.