How to enlarge a shape by a negative or minus scale factor from a centre of enlargement.

Updated on January 9, 2012

Before you attempt enlarging shaping with negative scale factors make sure you can enlarge shape with positive scale factors. In order to enlarge a shape with a negative scale factor:

a) First make sure that you have marked on the centre of enlargement onto your coordinate grid.

b) Next count the distance from the centre of enlargement to one of the corners of your shape.

c) Multiply these distances by your scale factor and change the directions. For example, if the distance from the centre of enlargement to one of your corners is 3 squares right and 7 squares up, and the scale factor of enlargement is -3, then the new directions will be 9 left and 21 down.

d) Next count out these new directions from the centre of enlargement and plot the corner of your enlarged shape.

e) Repeat this process for the other vertices.

Let’s take a look at an example of enlarging a shape with a negative scale factor.

Example 1

Enlarge the shape by a scale factor ×-2 from the centre of enlargement marked on the coordinate grid.

First let’s do the closest corner of the triangle.

The distance from the centre of enlargement to this corner is 1 right and 1 up.

So doubling these directions and reversing them you get 2 left and 2 down. Count these directions from the centre of the enlargement and mark on this corner onto the coordinate grid.

Next do the top corner of the triangle.

The distance from the centre of enlargement to this corner is 1 right and 2 up.

So doubling these directions and reversing them you get 2 left and 4 down. Count these directions from the centre of the enlargement and mark on this corner onto the coordinate grid.

Finally do the furthest corner away from the centre of the enlargement.

The distance from this corner to the centre of enlargement is 3 right and 1 up.

So doubling this distance and reversing the directions you get 6 left and 2 down. Mark this final corner onto the coordinate grid by counting from the centre of the enlargement.

Also notice that the new shape has been rotated 180⁰.

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