Enlargements

Sometimes, we like to make an object smaller or larger than its original size.

This is similar to rotation, in that we need to know two pieces of information:

• Centre of Enlargement (a point somewhere away from the image, usually the origin)
• Scale factor (usually called k)

The best way to do perform an enlargement is to count how far away each point on the object is from the centre of enlargement, and then multiply by the scale factor.

For example, look at the triangle ABC below.

We are going to enlarge from centre (0,0). As you can see, A is at the point (1,1). If we use scale factor 2, then A’ will be twice the distance of A from O. Luckily this is just (1,1) so you can easily located A’ at (2,2)! Have a look at points B and C and make sure you understand how that works.

HINT: If the centre of enlargement is the origin, it’s quite easy, just multiply the coordinates by the scale factor. But it won’t always be from the origin!

Note, that if we have a scale factor of less than 1 (i.e. a fraction), then the image will be smaller – in other words, a reduction.

Textbook Ex: (you should try and copy these onto paper for better results!)

ANSWERS BELOW

3a) (4.5, 6)
3b) (0,2)