Centre of enlargement

There is another part to enlarging shapes.

The centre of enlargement is a point from which an enlargement occurs

In the diagram, point O is going to be the centre of enlargement

We are going to draw line segments from O through each point on ABCD

We measure the distances OA, OB, OC and OD.

We place point A’ at twice the distance of OA from O along the line segment drawn through point A from O.

We do the same for all the other points.

The distance from O to A’ is twice that from O to A

OA’ = 2OA

Also

OB’ = 2OB

Similarly with OC’ and OD’.

We have produced an enlargement of ABCD by a scale factor of two.

A’B’ = 2AB

All the sides of square A’B’C’D’ are twice the size of the corresponding side of ABCD.

We have enlarged ABCD by a scale factor of 2 through centre of enlargement of (-2, -1).