Year 9 Enlargements and Scale Factors Worksheets & Practice

Worked examples

Year 9 enlargements and scale factors: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

1. Example 1 · Finding a missing side length using a scale factor

   Triangle $ABC$ is enlarged by a scale factor of $3$ to produce triangle $A'B'C'$. Triangle $ABC$ has side lengths $4$ cm, $6$ cm and $9$ cm. Find the side lengths of triangle $A'B'C'$.

   Show worked solution

   Key idea: Under an enlargement with scale factor $k$, every side length of the image is $k$ times the corresponding side length of the original shape.

   1. Multiply each side length by the scale factor $k = 3$:
      $\begin{gathered}4 \times 3 = 12 \text{ cm} \\ 6 \times 3 = 18 \text{ cm} \\ 9 \times 3 = 27 \text{ cm}\end{gathered}$
   2. The side lengths of triangle $A'B'C'$ are $12$ cm, $18$ cm and $27$ cm.

   Answer: $12$ cm, $18$ cm and $27$ cm.

2. Example 2 · Applying an enlargement on the coordinate plane

   Rectangle $ABCD$ has vertices $A(1, 1)$, $B(3, 1)$, $C(3, 2)$ and $D(1, 2)$. It is enlarged by a scale factor of $4$ from the centre of enlargement at the origin $(0, 0)$. Find the coordinates of the image $A'B'C'D'$.

   Show worked solution

   Key idea: To enlarge from the origin by scale factor $k$, multiply every coordinate by $k$.

   1. Multiply each coordinate by $4$:
      $\begin{aligned} A(1,1) &\to A'(4, 4) \\ B(3,1) &\to B'(12, 4) \\ C(3,2) &\to C'(12, 8) \\ D(1,2) &\to D'(4, 8) \end{aligned}$
   2. Check one side length to confirm: $AB = 3 - 1 = 2$ units; $A'B' = 12 - 4 = 8$ units; $8 = 2 \times 4$. ✓

   Answer: $A'(4,4)$, $B'(12,4)$, $C'(12,8)$, $D'(4,8)$.

3. Example 3 · Scale factor and area in a real-life context

   A landscape architect is designing two similar rectangular gardens. The smaller garden measures $3$ m by $5$ m. She enlarges the design by a scale factor of $3$ to create the larger garden. How much larger is the area of the bigger garden than the area of the smaller garden? Give your answer in square metres.

   Show worked solution

   Key idea: When a shape is enlarged by scale factor $k$, its area is multiplied by $k^2$.

   1. Find the area of the smaller garden:
      $3 \times 5 = 15 \text{ m}^2$
   2. Find the area of the larger garden using the scale factor:
      $\text{Area of larger garden} = 15 \times 3^2 = 15 \times 9 = 135 \text{ m}^2$
   3. Find how much larger the bigger garden is:
      $135 - 15 = 120 \text{ m}^2$

   Answer: The larger garden has an area $120$ m$^2$ greater than the smaller garden.

Common mistakes

Where students usually lose marks

Try one yourself

Your turn

Got a different enlargements and scale factors question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.