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Maths

Transformation and enlargements - Higher

We are going to be looking at:

Enlargements - fractional and negative scale factors

We already know how to draw an enlargement with a positive whole number scale factor. If you need to revise this, return to Transformations: Enlargements. We are now going to look at how this method applies to fractional and negative scale factors.

Fractional scale factors

If we 'enlarge' a shape by a scale factor that is between -1 and 1, the image will be smaller than the object

Question

Enlarge triangle ABC with a scale factor 1/2, centred about the origin.

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Answer
image: a graph with an x axis of 0 to 5 and a y axis of 0 to 6. A triangle is plotted with corners labelled a, b and c.

The scale factor is 1/2, so:

OA' = 1/2OA

OB' = 1/2OB

OC' = 1/2OC

Since the centre is the origin, we can in this case multiply each coordinate by 1/2 to get the answers.

A = (2, 2), so A' will be (1, 1).

B = (2, 6), so B' will be (1, 3).

C = (4, 2), so C' will be (2, 1).

Negative scale factors

An enlargement using a negative scale factor is similar to an enlargement using a positive scale factor, but this time the image is on the other side of the centre of enlargement, and it is upside down.

Question

Enlarge the rectangle WXYZ using a scale factor of - 2, centred about the origin.

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Answer
image: a graph with an x axis of minus 6 to 3 and a y axis of minus 4 to 3. Two squares are plotted with corners labelled w, x, y and z.

The scale factor is -2, so multiply all the coordinates by -2. So OW' is 2OW. This time we extend the line WO beyond O, before plotting W'.

In a similar way, we extend XO, YO and ZO and plot X',Y' and Z'. Can you see that the image has been turned upside down?

Back to Geometry and measures index

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