🔍 Zoom It Right: Mastering Enlargement at Any Scale!

Whether you are mapping a tiny sketch onto a whiteboard or reducing a photograph for your notebook, **enlargement** (also called scaling) is an indispensable transformation in O-Level Mathematics. Mastering it helps you handle coordinate geometry questions, interpret maps, and even design graphics—skills that show up on exam papers and in real life!

Core Idea: What Is Enlargement?

An enlargement changes the size of a shape while preserving its angle measures and proportion of sides. The transformation is defined by a *centre of enlargement* and a *scale factor*

k

. A **positive**

k

keeps the image on the same side of the centre, while a **negative**

k

flips it to the opposite side.

Scale factor $k>1$ ⇒ image is bigger than the object.
Scale factor $0<k<1$ ⇒ image is a reduction.
Scale factor $k<0$ ⇒ image is enlarged/reduced and reflected through the centre.

Worked Example: Triangle Blow-Up

Problem: Triangle ABC has vertices A(1,2), B(3,1), and C(2,4). Enlarge the triangle by a scale factor of

k=-2

about the centre O(0,0). Give the coordinates of A′, B′, C′ and sketch the image.

Step 1: Write vector form for each vertex from the centre
$\vec{OA}=\begin{pmatrix}1\\2\end{pmatrix},\; \vec{OB}=\begin{pmatrix}3\\1\end{pmatrix},\; \vec{OC}=\begin{pmatrix}2\\4\end{pmatrix}.$
Step 2: Multiply by the scale factor $k=-2$ to get image vectors
$\vec{OA'}=-2\vec{OA}=\begin{pmatrix}-2\\-4\end{pmatrix},\; \vec{OB'}=-2\vec{OB}=\begin{pmatrix}-6\\-2\end{pmatrix},\; \vec{OC'}=-2\vec{OC}=\begin{pmatrix}-4\\-8\end{pmatrix}.$
Step 3: Extract coordinates ⇒ A′(-2, -4), B′(-6, -2), C′(-4, -8). Plot these points and join them to see a triangle twice as large and reflected through O.

Like any skill, **practice makes perfect**. Draw different shapes, pick random centres, and test both positive and negative scale factors. Soon you will enlarge any figure confidently, ace your exam, and apply these scaling skills beyond the classroom!