Transformation and enlargements - Higher
We are going to be looking at:
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.
If we 'enlarge' a shape by a scale factor that is between -1 and 1, the image will be smaller than the object
Enlarge triangle ABC with a scale factor 1/2, centred about the origin.
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).
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.
Enlarge the rectangle WXYZ using a scale factor of - 2, centred about the origin.
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?
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