How to Enlarge a Shape with a Fractional Scale Factor

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 13 about the center of enlargement (1, 1).

Step-by-Step:

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.

2

Draw a line from the center 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 center of enlargement (or 3 units across and 3 up).

4

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).

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 13, the enlarged shape is a 13 of the size and a 13 the distance from the center of enlargement.

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See Also

What is geometry? What are transformations? What is a scale factor? What is a fraction? What are Cartesian coordinates? What is the x-axis? What is the y-axis? Enlarging a shape with a negative scale factor