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# 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).

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'**.**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.

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