Home · IGCSE Maths 0580 · Transformations and vectors · Enlargement and translation · Practice
IGCSE · Practice questions · Enlargement and translation

Scale factors and vectors.

Six original Cambridge-style questions on enlargement and translation: drawing images by coordinates and describing single transformations fully.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
The method

Measure from the centre; move by the vector.

01
Recall
[1 marks]

A translation maps the point \((2, 5)\) onto \((7, 3)\). Write down the column vector of the translation.

  • \(7 - 2 = 5\) across, \(3 - 5 = -2\) up: \(\begin{pmatrix}5\\-2\end{pmatrix}\). ✓
02
Calculation
[2 marks]

Triangle \(T\) has vertices \((1, 1)\), \((2, 1)\), \((1, 3)\). Find the vertices of its image after an enlargement, scale factor 3, centre \((0, 0)\).

  • Multiply each coordinate by 3. ✓
  • \((3, 3)\), \((6, 3)\), \((3, 9)\). ✓
03
Calculation
[3 marks]

Triangle \(U\) has vertices \((6, 4)\), \((10, 4)\), \((6, 8)\). Find the vertices of its image after an enlargement, scale factor \(\dfrac{1}{2}\), centre \((2, 0)\).

  • Steps from \((2, 0)\): \(\begin{pmatrix}4\\4\end{pmatrix}\), \(\begin{pmatrix}8\\4\end{pmatrix}\), \(\begin{pmatrix}4\\8\end{pmatrix}\). ✓
  • Halve them: \(\begin{pmatrix}2\\2\end{pmatrix}\), \(\begin{pmatrix}4\\2\end{pmatrix}\), \(\begin{pmatrix}2\\4\end{pmatrix}\). ✓
  • Add to \((2, 0)\): \((4, 2)\), \((6, 2)\), \((4, 4)\). ✓
04
Analysis
[3 marks]

Triangle \(A\) has vertices \((1, 2)\), \((3, 2)\), \((1, 3)\). Triangle \(B\) has vertices \((3, 4)\), \((9, 4)\), \((3, 7)\).

Describe fully the single transformation that maps \(A\) onto \(B\).

  • Horizontal sides: \(3 - 1 = 2\) and \(9 - 3 = 6\), so the scale factor is 3. ✓
  • Line through \((1, 2)\) and \((3, 4)\): \(y = x + 1\), which passes through \((0, 1)\). Line through \((3, 2)\) and \((9, 4)\): gradient \(\dfrac{1}{3}\), and at \(x = 0\) it gives \(y = 2 - 1 = 1\). They meet at \((0, 1)\). ✓
  • Enlargement, scale factor 3, centre \((0, 1)\). ✓
05
Calculation
[2 marks]

(Extended) Triangle \(V\) has vertices \((2, 1)\), \((4, 1)\), \((4, 2)\). Find the vertices of its image after an enlargement, scale factor \(-\dfrac{1}{2}\), centre \((0, 0)\).

  • Multiply each coordinate by \(-\dfrac{1}{2}\). ✓
  • \((-1, -0.5)\), \((-2, -0.5)\), \((-2, -1)\): half the size, on the other side of the origin, upside down. ✓
06
Analysis
[4 marks]

A robot moves on a warehouse floor marked with a coordinate grid. It starts at \((4, 1)\). It is translated by \(\begin{pmatrix}3\\-2\end{pmatrix}\) and then by \(\begin{pmatrix}-5\\4\end{pmatrix}\).

(a) Find the robot's final position.

(b) Write down the single column vector that would have moved it there in one step.

(c) Write down the column vector that takes it from its final position back to the start.

  • (a) \((4 + 3, 1 - 2) = (7, -1)\), then \((7 - 5, -1 + 4) = (2, 3)\). ✓
  • (b) \(3 + (-5) = -2\) and \(-2 + 4 = 2\): \(\begin{pmatrix}-2\\2\end{pmatrix}\). ✓
  • (c) The reverse move: \(\begin{pmatrix}2\\-2\end{pmatrix}\). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.