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Maths

Transformations

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Enlargements

When working out enlargements, you will need to know the scale factor and centre of enlargement.

  • The scale factor tells us by how much the object has been enlarged.
  • The centre of enlargement tells us where the enlargement is being measured from.

Example:

image: two triangles, the smaller is 1 3rd the size of the larger triangle. The smaller triangle is marked Q, P and R. The larger triangle is marked Q', P' and R'.

P'Q' = 3 × PQ

Q'R' = 3 × QR

P'R' = 3 × PR

Therefore, we say that the transformation is an enlargement with scale factor 3.

You may be asked to enlarge a shape with a given centre of enlargement. Look through this slideshow to see an example.

To enlarge an object, scale factor 2.

The object is triangle ABC

enlargement 1

The centre of enlargement is O.

To enlarge an object, scale factor 3.

This method is identical to the previous one, but

OA' = 3 × OA

OB' = 3 × OB

OC' = 3 × OC

The centre of enlargement is not always outside the object. Look at the following examples:

The next diagram shows an enlargement, scale factor 3. The centre of enlargement, X, is also a point of the object WXYZ. The result is that X' is in the same place as X.

image: an example of an enlargement with a scale factor of 3

The next diagram shows an enlargement, scale factor 2, centre O, where O is inside the object. The result is that the image surrounds the object.

image: an example of an enlargement with a scale factor of 2

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