Page 163 - MAT KS3 Y8 Cambridge CheckPoint

16.2 Enlarging shapes

16.2 Enlarging shapes image

An enlargement of a shape is a copy of the shape that changes the lengths, but
object
keeps the same proportions. In an enlargement all the angles stay the same size. 4 cm
Look at these two rectangles. 2 cm
The image is an enlargement of the object. Every length on the image is twice
as long as the corresponding length on the object. 1 cm 2 cm
The scale factor is 2.
The centre of enlargement tells you where to draw the
image on a grid. In this case, as the scale factor is 2, not
only must the image be twice the size of the object, it must
3 cm
be twice the distance from the centre of enlargement.
centre of
enlargement
6 cm

You can check you have drawn an enlargement
correctly by drawing lines through the
corresponding corners of the object and image.
The lines should all meet at the centre of the
enlargement. This is also a useful way to find the
centre of enlargement if you are only given the centre of
object and the image. enlargement

Worked example 16.2

Draw enlargements of the following triangles using the given scale factors and centres of enlargements.
a scale factor 2 b scale factor 3

a Start by looking at the corner of the triangle that is closest to the
centre of enlargement (COE). This corner is 1 square to the right of
the COE, so with a scale factor of 2, the image will be 2 squares to
the right of the COE. Plot this point on the grid, then complete the
triangle, remembering to double all the other lengths.
b One of the corners of this triangle is on the centre of enlargement,
so this corner doesn’t move. Look at the bottom right corner of the
triangle. This corner is 1 square to the right and 1 square down from
the COE. With a scale factor of 3, the image will be 3 squares to the
right and 3 squares down from the COE. Plot this point on the grid
then complete the triangle, remembering to multiply all the other
lengths by 3.

16 Position and movement 161