Enlargements

Last one of these - honest

Most complicated transformation

• Can make the shape larger or smaller in size.

• The position of the centre of enlargement determines where the image will be, the scale factor determines the size.

Keywords

• Scale factor – the amount of times the lengths of the shape are increased by.

• Centre of enlargement – the point the enlargement takes place from

Simplest case

No centre of enlargement, just make the shape bigger

Enlarge shape by a scale factor of 3

Object image

Just make all the lengths 3 times longer.

That wasn’t difficult.

Well let’s add the centre of enlargement

Enlarge the object by a scale factor of 2 from the centre of enlargement object image

A A’

o

B C

B’ C’

oB’ = 2oB A’B’ = 2AB

That wasn’t easy!

• Measure the distance from the centre of enlargement to the first corner of the object.

• Double this distance (for scale factor 2) and then draw a line that long from the c. of E. passing through the point on the object.

• At the end of this line is the corresponding point on the image.

• Repeat for the remaining points.

Show me.Enlarge shape by s.f. of 2

o

• From o to A = 3cm so oA’ will be 6cm.

• Draw a 6cm line from o passing through A.

• At the end of this line is A’

• Repeat for the other points.

3cm6cm

A’

A

A few more important points

Don’t rub out your construction lines

Almost there now

If a shape is enlarged by a scale factor,k, then the area of the image is k2 larger than that of the object.

The inverse of an enlargement of scale factor, k is….

An enlargement of scale factor 1/k from the same centre of enlargement.

If the scale factor was 2/3 the inverse would be an enlargement by a scale factor of 3/2

The end

Any questions?