In this section we consider enlargements. We look at the use of the terms 'scale factor' and 'centre of enlargement'.
The rectangle A, shown below, has been enlarged to give the shapes B, C and D.
Write down the scale factor for each enlargement.
A to B is scale factor 2 because the lengths are doubled.
A to C is scale factor because the lengths are halved.
A to D is scale factor 2.5 because the lengths are 2.5 times longer.
A rectangle has sides of lengths 2 cm and 3 cm. It is enlarged with scale factor 3.
Draw the original rectangle and the enlarged rectangle.
|3 × 2 cm = 6 cm|
|3 × 3 cm = 9 cm|
Examples 3 and 4 show how to use a centre of enlargement when enlarging a shape.
The diagram shows the triangle A B C and the point O.
Enlarge the triangle with scale factor 3, using O as the centre of enlargement.
The diagram shows the 2 triangles; the explanation follows.
First draw lines from point O through A, B and C, as shown in the diagram.
Measure the length O A and multiply it by 3 to get the distance from O of the image point A', i.e. O A' = 3 × O A. Mark the point A' on the diagram.
The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.
The following diagrams show two shapes that have been enlarged. Determine the centre of enlargement in each case.
To find the centres of enlargement, draw lines through the corresponding corners of each shape. These lines will cross at the centre of enlargement, as shown below. The centres have been marked with the letter O in both diagrams.