Enlargement
Enlarging a shape changes its size.
All the sides of the triangle X'Y'Z' are twice as long as the sides of the original triangle XYZ. The triangle XYZ has been enlarged by a The ratio of corresponding lengths in similar shapes, ie how much larger or smaller the shapes are. of 2.
Enlargement is an example of a transformation. A transformation is a way of changing the size or position of a shape.
To enlarge a shape, a centre of enlargement is required. When a shape is enlarged from a centre of enlargement, the distances from the centre to each point are multiplied by the scale factor.
The lengths in triangle A'B'C' are 3 times as long as triangle ABC. The distance from O to triangle A'B'C' is 3 times the distance from O to ABC.
The triangle ABC has been enlarged by a scale factor of 3 about the centre of enlargement O.
Positive enlargements
A positive scale factor increases the size of a shape.
Example
Image caption, Enlarge the triangle ABC by a scale factor of 2 about the centre of enlargement O
1 of 4
Alternatively, the distances OA, OB and OC can be shown as vectors. OA = \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) so under a scale factor of 2 OA' = \(\begin{pmatrix} 6 \\ 4 \end{pmatrix}\).
The centre of enlargement may be outside an object, or it may be inside a shape, on an edge or at a corner.
The image may overlap the shape or one may be inside the other.
Question
Enlarge the triangle PQR by a scale factor of 3 about the centre of enlargement O.
First draw ray lines from O to each corner of the triangle and extend them.
Next, measure the distance from O to each corner of PQR. Multiply this distance by 3 and plot the points P' Q' and R'.
Finally join up the points P' Q' R'.
Question
What scale factor has been used to enlarge the shape OXYZ to OX'Y'Z'?
Each side in the shape OX'Y'Z' is twice as long as the side in the shape OXYZ.
OXYZ has been enlarged by a scale factor of 2 about the centre of enlargement O.
