An enlargement is a transformation where the size of an object changes.
The object becomes larger or smaller.
If points on the object and the corresponding points on the image are joined with a straight line, these straight lines meet at the centre of enlargement.
The scale factor for an enlargement tells how much an object has been enlarged by.
In the diagram opposite, the scale factor is 2
- each part of the image is twice the size of the same part on the object
- each point on the image is twice as far from the centre of enlargement as the same point on the object
The diagram shows an enlargement, centre O with ascale factor of 2.
To see examples of other enlargements −
Properties of Enlargement
The diagram below shows an enlargement of scale factor 3
Each point on the image is 3 times the distance from the centre of enlargement as the corresponding point on the object.Each line on the image A'B'C'D' is 3 times the length of the corresponding lines on the object ABCD
e.g. B'C' = 9cm and BC = 3 cm
e.g. OD' = 15 cm and OD = 5 cm
Therefore the scale factor is 3
- The scale factor =
- The centre of enlargement is the only point that does not move (invariant)
- The shape of the object does not change when enlarged
- The sizes of the angles in the object and image do not change (invariant)
Scale Factor is a Fraction
Enlargements can have fractional scale factors i.e. Less than 1
The diagram opposite shows an enlargement, centre O.
The image is half the size of the object.
Using object and image lengths
Scale Factor= 5 /10 = 0.5
Using distances from centre of enlargement
Scale factor = 9/18 = 0.5