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.

Question

Enlarge the shape below by a scale factor of 1⁄3 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.
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.

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 3 diagonal units from the centre of enlargement (or 3 units across and 3 up).

4

Multiply this distance (3) by the scale factor (1⁄3).

Scaled distance = Distance × Scale factor

Scaled distance = 3 diagonal units × 1⁄3

Scaled distance = 1 diagonal unit

The distance to the transformed point is 1 diagonal unit (or 1 unit across and 1 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'.
We have transformed point 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 1⁄3, the enlarged shape is a 1⁄3 of the size and a 1⁄3 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.