Centre of enlargement

The position of the enlarged shape is described by the centre of enlargement (O in the following diagrams).

The triangles above have been enlarged using the same scale factor (scale factor of 3). Their positions in relation to the small triangles are different because the centres of enlargement are different.

Example

The slideshow below shows how triangle ABC is enlarged with a scale factor of 2 and centre of enlargement O:

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Image caption,
Enlarge triangle with a scale factor of 2 and centre of enlargement O
A line is drawn from the point O through point A of the triangle.
Image caption,
Enlarging a triangle with a scale factor of 2
Similarly, extend lines from the point O through points B and C.
Image caption,
Enlarging a triangle with a scale factor of 2
Points A', B' and C' are drawn, so that: OA' = 2 × OA, OB' = 2 × OB, OC' = 2 × OC.

For a scale factor of 2:

OA' = 2 × OA

OB' = 2 × OB

OC' = 2 × OC

For a scale factor of 3:

OA' = 3 × OA

OB' = 3 × OB

OC' = 3 × OC

The centre of enlargement can be either outside or within the original shape.

Question

What are the scale factors of enlargement for shapes A and B?

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Linear scale factorCentre of enlargement