How to Enlarge a Shape with a Negative Scale Factor

Enlarging a Shape with a Negative Scale Factor

A shape can be enlarged with a negative scale factor.

If the scale factor is negative, the shape is enlarged on the other side of the center of enlargement and it is turned upside down.

How to Enlarge a Shape with a Negative Scale Factor

Enlarging a shape with a negative scale factor is easy.

Question

Enlarge the shape below by a scale factor of −2 about the center of enlargement (5, 5).

Step-by-Step:

1

Plot the center of enlargement.

In our example, the Cartesian coordinates of the center of enlargement is (5, 5). It is 5 units along the x-axis and 5 units 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 point A to the center of enlargement.

Note: It is useful to extend the line beyond the center of enlargement.

3

Measure the length of the line from the point to the center of enlargement.

In our example, the point is 1 diagonal unit from the center of enlargement (or 1 unit across and 1 up).

4

Multiply this distance (2) by the scale factor. Ignore the − sign in front of the scale factor for now.

Scaled distance = Distance × Scale factor

Scaled distance = 1 diagonal units × 2

Scaled distance = 2 diagonal units

The distance to the transformed point is 2 diagonal units.

Now we use the − sign in the scale factor.

Because the scale factor is negative, the distance will be on the other side of the center of enlargement. The 2 diagonal units will be 2 units to the left and 2 units down.

5

Measure the distance found in Step 4 along the line drawn in Step 2. Measure it from the center of enlargement going away from the shape.

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 −2, the enlarged shape is 2 times larger and 2 times the distance from the center of enlargement. It is also the other side of the center of enlargement and turned upside down.

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See Also

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