Recognise and Describe Negative and Fractional Enlargements

In this activity, we will recognise and describe enlargements where the scale factor is negative or fractional!

First, let's recap with positive whole number (integer) scale factors!

Example

Enlarge the shape A by scale factor 2, from the centre of enlargement X. 

Answer

We take each vertex (corner) and look at the distance.

This one is 1 right and 1 down from the centre.

To enlarge it, we multiply the distance by the scale factor (2) 

We go 1 x 2 = 2 right and 1 x 2 = 2 down, x is the new vertex.

Complete the other two vertices in the same way.

Finally, join up the three new vertices!

An enlargement of scale factor 2 from the centre X

Let's look at a fractional scale factor.

Even when the scale factor is a fraction and we can see that it would make the shape smaller, as it is less than 1, it is still called an enlargement - strange, isn't it?!

Example

Enlarge the shape below by scale factor 1/2 from the centre X

Answer

Firstly, the sides of the new (enlargement) square will be multiplied by the scale factor 1/2

So, each side of the square will be 1 unit long.

To find the correct position, we have to halve the distance of each vertex. Let's start with the nearest.

This one is 4 across and 2 down

Scale factor is 1/2

So, we multiply by 1/2

Leaves us with 4 x 1/2 = 2 across

2 x 1/2 = 1 down

As we know the sides are 1 unit long, if we have the correct position of the first vertex, we could draw it from there.

It saves plotting all four vertices.

It looks like this:

Let's try a negative scale factor!

For these we do the opposite!

With a scale factor of -2

If the vertex is 3 right and 2 down from the centre, we move the opposite way for a negative:

3 RIGHT to 3 x 2 = 6 LEFT 

2 DOWN to 2 x 2 = 4 UP

Let's do a question.

Enlarge the shape below by scale factor -2 from the centre X

Answer

It is scale factor -2 so all the sides of the enlargement are 2 times longer.

It is negative, so we do the opposite movements for each corner (vertex).

The nearest vertex is 1 left and 1 up

The new one will be opposite and x 2

1 left becomes 2 right

1 up becomes 2 down

You can now do each vertex the same way or you can draw it in from there as you have the position by finding the nearest point.

It is upside down and twice as long!

Let's give some of these a go!