# Enlarging a Shape(KS3, Year 7)

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## Enlarging a Shape

A shape can be enlarged. It can be made larger or smaller.

## How to Enlarge a Shape

Enlarging a shape is easy.

## Question

Enlarge the shape below by a scale factor of 3 about the centre of enlargement (1, 1).

## 1

Plot the centre of enlargement. In our example, the Cartesian coordinates of the centre of enlargement is (1, 1). It is 1 unit along the x-axis and 1 unit up the y-axis.
Each point on the shape is enlarged by the same amount. Let us choose a point on the shape and transform it. We will transform point A.

## 2

Draw a line from the centre of enlargement to point A.Note: It is useful to extend the line beyond the point.

## 3

Measure the length of this line. In our example, the point is 1 diagonal unit from the centre of enlargement (or 1 unit across and 1 up).

## 4

Multiply this distance (1) by the scale factor (3).

Scaled distance = Distance × Scale factor

Scaled distance = 1 diagonal unit × 3

Scaled distance = 3 diagonal units

The distance to the transformed point is 3 diagonal units (or 3 units across and 3 up).

## 5

Measure the distance found in Step 4 along the line drawn in Step 2. This is the point on the enlarged shape, which we will call A'.
We have transformed point A to point A' on the enlarged shape. Repeat for points B and C.

With all the vertices (corners) of the shape transformed, the enlarged shape can be drawn:

By multiplying the shape by a scale factor of 3, the enlarged shape is 3 times larger and 3 times the distance from the centre of enlargement.

## Lesson Slides

The slider below shows another real example of how to enlarge a shape.

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## Scale Factor

If the scale factor is greater than 1, the enlarged shape gets bigger: If the scale factor is less than 1, the enlarged shape gets smaller: If the scale factor is equal to 1, the enlarged shape stays the same size:

## What Is an Enlargement?

An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.

## Enlarged Shapes Are Similar Shapes...

If a shape is enlarged, the shapes are similar. Similar shapes are the same shape but not the same size.

## ...But Not Congruent Shapes

Congruent shapes are the same shape and the same size. If a shape has only been translated, reflected or rotated (or some combination of all three) then the shape is congruent.