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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:

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

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.

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.

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