📏 Grow It Right: Mastering Enlargement with Integer Scale Factors!

Enlargement is a core transformation skill that appears frequently in O-Level exam papers. Being able to recognise, describe and perform an **accurate enlargement** helps you secure easy marks in geometry questions and underpins later topics such as similarity and trigonometry.

What Is Enlargement?

An enlargement scales a shape by a *positive integer* factor

k

from a fixed point called the *centre of enlargement*. Key facts: • All corresponding angles stay the same (shape is similar). • All lengths are multiplied by

k

. • The area is multiplied by

k^2

and the volume (if 3-D) by

k^3

. • Lines joining the centre to each vertex stay on the same straight line after enlargement. Remember: **If

k=1

the figure is unchanged; if

k>1

the figure gets bigger.**

Worked Example: Stretching a Triangle

Problem: Triangle

ABC

has vertices

A(1,2)

B(3,1)

and

C(2,4)

. Enlarge it with centre

(0,0)

and scale factor

k=3

. Step-by-step solution: 1. Draw rays from

(0,0)

through each original vertex. 2. Calculate new coordinates by multiplying each coordinate by

k=3

: •

A'(3,6)

(

1\times3

2\times3

) •

B'(9,3)

(

3\times3

1\times3

) •

C'(6,12)

(

2\times3

4\times3

) 3. Plot

A',B',C'

and join them to form the enlarged triangle. 4. Quick check: the side lengths should be exactly three times the original lengths.

Now that you know the rules, practise by picking random shapes and centres on graph paper, then enlarge them with different integer factors. The more you draw, the faster you’ll earn those transformation marks on exam day!