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.


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


Draw a line from the centre of enlargement to point A.

Note: It is useful to extend the line beyond the point.


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).


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).


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. Open the slider in a new tab
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See Also

What is geometry? What are transformations? What is a scale factor? What are Cartesian coordinates? What is the x-axis? What is the y-axis?