Year 9AC9M9SP02

Enlargement and What It Preserves

Apply the enlargement transformation to shapes and objects; identify and explain aspects that remain the same and those that change.

An enlargement changes size but not shape. Knowing exactly what survives is what the question is really testing.

Method

Scale factor multiplies every length

k

Distances from the centre scale too.

Angles never change

This is why the image stays similar to the original.

Area scales by $k^2$

Not by $k$. The single commonest error.

Volume scales by $k^3$

$k$ under 1 makes it smaller

0 < k < 1

Still called an enlargement.

e.g.

\text{A rectangle } 3 \times 5 \text{ is enlarged by scale factor } 4. \text{ What changes?}

Multiply each length by the scale factor. $12 \times 20$
Compare the angles. All were 90 degrees. $\text{still } 90^\circ \text{ — unchanged}$
Find the original area. $3 \times 5 = 15$
Find the new area. $12 \times 20 = 240$
Compare them. $\frac{240}{15} = 16 = 4^2$
Conclude: lengths $\times 4$ , area $\times 16$ , angles unchanged.

State what changed and what did not. Both halves earn marks.

\text{Scale factor } 3. \text{ What happens to area?}

Answer

\times 9

\text{Scale factor } 5. \text{ What happens to volume?}

Answer

\times 125

\text{Area grows } \times 36. \text{ Find the scale factor.}

Answer

k = 6

\text{Does an enlargement change the angles?}

Answer

\text{No.}

\text{Is } k = \tfrac{1}{2} \text{ an enlargement?}

Answer

\text{Yes, a reduction — still called enlargement.}

\text{Original and image: are they congruent or similar?}

Answer

\text{Similar, unless } k = 1.