Enlarging a Shape with a Fractional Scale Factor

A shape can be enlarged with a scale factor. Usually, this makes the shape larger. If the scale factor is a fraction (between 0 and 1), the enlargement makes the shape smaller.

How to Enlarge a Shape with a Fractional Scale Factor

Enlarging a shape with a fractional scale factor is easy.


Enlarge the shape below by a scale factor of 13 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 3 diagonal units from the centre of enlargement (or 3 units across and 3 up).


Multiply this distance (3) by the scale factor (13).

Scaled distance = Distance × Scale factor

Scaled distance = 3 diagonal units × 13

Scaled distance = 1 diagonal unit

The distance to the transformed point is 1 diagonal unit (or 1 unit across and 1 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 13, the enlarged shape is a 13 of the size and a 13 the distance from the centre of enlargement.

Lesson Slides

The slider below shows another real example of how to enlarge a shape with a fractional scale factor.