# Enlarging a Shape

(KS3, Year 7)

## 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).## Step-by-Step:

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

Scaled distance = Distance × Scale factor

Scaled distance = 1 diagonal unit × 3

Scaled distance = 3 diagonal units

## 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'**.**A**to point

**A'**on the enlarged shape. Repeat for points

**B**and

**C**.

## Answer:

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.

## Top Tip

## 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**:

## Note

## 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.