How to Enlarge a Shape

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 center of enlargement (1, 1).



Plot the center of enlargement.

In our example, the Cartesian coordinates of the center 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 center 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 center 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 center of enlargement.


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

Open the slider in a new tab

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?