We consider two types of question with “Enlargements”.

• IDENTIFICATION: One is where we are given a shape that has been transformed and we want to identify the transformation (for an enlargement we must identify both the centre and the scale factor of the enlargement. If the image is a different size to the original shape, then an enlargement must have taken place (this is the only geometrical transformation we study at iGCSE which changes the size of the shape.
• EXECUTION: The other is where we are given a shape and told a centre and a scale factor of enlargement and our job is to “do” the enlargement to the shape to find out where the image will be.

IDENTIFICATION

We draw extended lines joining the vertices of the shape with the corresponding vertices of the image. Where these lines intersect is the centre of enlargement.

To find the scale factor, we can measure the distance from the centre of enlargement to a vertex of the shape (S) and from the centre of enlargement to a vertex of the image (I). If we divide the second number by the first number (i.e. I/S, we get the scale factor). If our shape and image are on a Cartesian grid, then instead of measuring we can calculate the distance using Pythagoras’ theorem with horizontal and vertical distances (or often simply by looking at the line and noticing that it is twice as long, for instance).

If the image is smaller than the shape, the scale factor will be less than 1 (e.g. 0.5). If the image has moved to the opposite side of the shape and is oriented in the opposite direction, the scale factor will be negative (e.g -2)

Worked Example

EXECUTION

This is in many ways easier than IDENTIFICATION. We measure out a line from the centre through each of the vertices which is n-times longer than the distance from the centre to the vertex, where n is the scale factor. If the scale factor is negative, we measure it in the opposite direction to the corresponding vertex. If our shape is on a set of coordinate axes, we can apply it to the horizontal distance and the vertical distance separately instead.

Worked Example

Exercise

Answers