Negative enlargement

Higher only

The idea

A negative scale factor enlarges through the centre: the image is on the opposite side and upside down. Scale factor $-2$ doubles each distance from the centre in the opposite direction.

Find the vector from the centre to each vertex.
Multiply it by the scale factor (which reverses it).
Plot from the centre and join the new vertices.

Watch out The image goes on the other side of the centre.

See it worked

Worked exampleNon-calculator4 marks

The point $P(4, 3)$ is enlarged by scale factor $-2$ with centre $C(1, 1)$ .

(a) Find the coordinates of the image of $P$ .

(b) Describe fully the single transformation that maps the image back onto $P$ .

(a) From the centre to $P$ . $(4, 3) - (1, 1) = (3, 2)$
Multiply by $-2$ : the image is on the other side of the centre, twice as far. $-2 \times (3, 2) = (-6, -4)$
Add to the centre. $(1, 1) + (-6, -4) = (-5, -3)$
(b) The inverse of scale factor $-2$ is $-\frac{1}{2}$ , about the same centre.

Answer (a) $(-5, -3)$ ; (b) Enlargement, scale factor $-\frac{1}{2}$ , centre $(1, 1)$

Your turn

Question 1Non-calculator4 marks

Point P(5, 3) is enlarged by scale factor $-2$ with centre C(2, $-1$ ). Work out the coordinates of the image of P.

Question 2Non-calculator5 marks

An enlargement maps A $(6,3)$ to A′ $(-4,-7)$ with scale factor $-3/2$ .

(a) Find the centre of enlargement.

(b) A side has original length 8 cm. Find its image length.

Question 3Non-calculator5 marks

An enlargement maps A $(6,3)$ to A′ $(-10,-13)$ with scale factor $-3$ .

(a) Find the centre of enlargement.

(b) A side has original length 8 cm. Find its image length.

In past papers

18 official questions in 18 papers since 2017. The latest:

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