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IGCSE · Practice questions · Reflection and rotation

Mirror lines and centres.

Six original Cambridge-style questions on reflections and rotations: 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

Flipped or turned? Then give every fact.

01
Recall
[2 marks]

Write down the image of

(a) \((2, -3)\) after reflection in the \(y\)-axis

(b) \((4, 1)\) after reflection in the line \(y = 2\).

  • (a) \((-2, -3)\) ✓
  • (b) \((4, 1)\) is 1 unit below \(y = 2\), so its image is 1 unit above: \((4, 3)\). ✓
02
Calculation
[2 marks]

Triangle \(T\) has vertices \((1, 1)\), \((4, 1)\) and \((4, 2)\).

Find the vertices of the image of \(T\) after a rotation of \(90^\circ\) anticlockwise about the origin.

  • \((x, y) \to (-y, x)\). ✓
  • \((1, 1) \to (-1, 1)\), \((4, 1) \to (-1, 4)\), \((4, 2) \to (-2, 4)\). ✓
03
Calculation
[2 marks]

Triangle \(T\) has vertices \((1, 1)\), \((4, 1)\) and \((4, 2)\).

Find the vertices of the image of \(T\) after reflection in the line \(x = -1\).

  • \((1, 1)\) is 2 right of \(x = -1\), so it goes to \((-3, 1)\). ✓
  • \((4, 1)\) and \((4, 2)\) are 5 right, so they go to \((-6, 1)\) and \((-6, 2)\). ✓
04
Analysis
[4 marks]

Shape \(P\) has vertices \((2, 1)\), \((5, 1)\), \((5, 3)\).

(a) Shape \(Q\) has vertices \((2, -1)\), \((5, -1)\), \((5, -3)\). Describe fully the single transformation that maps \(P\) onto \(Q\).

(b) Shape \(R\) has vertices \((-2, -1)\), \((-5, -1)\), \((-5, -3)\). Describe fully the single transformation that maps \(P\) onto \(R\).

  • (a) \(x\) unchanged, \(y\) changes sign: reflection in the \(x\)-axis (\(y = 0\)). ✓
  • (b) Both coordinates change sign: rotation, \(180^\circ\), about the origin \((0, 0)\). ✓
05
Analysis
[3 marks]

(Extended) Triangle \(A\) has vertices \((1, 1)\), \((3, 1)\), \((1, 2)\). Triangle \(B\) has vertices \((-1, -1)\), \((-1, -3)\), \((-2, -1)\).

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

  • Each point \((a, b)\) maps to \((-b, -a)\): for example \((3, 1) \to (-1, -3)\). ✓
  • The midpoint of \((3, 1)\) and \((-1, -3)\) is \((1, -1)\), which lies on \(y = -x\); \((1, 1)\) and \((-1, -1)\) give \((0, 0)\), also on it. ✓
  • Reflection in the line \(y = -x\). ✓
06
Analysis
[4 marks]

(Extended) A designer draws a flag shape \(F\) with vertices \((2, 1)\), \((4, 1)\), \((4, 2)\). She rotates it \(90^\circ\) clockwise about the point \((1, -1)\) to make shape \(G\).

(a) Find the vertices of \(G\).

(b) Describe fully the single transformation that maps \(G\) back onto \(F\).

  • (a) From \((1, -1)\): \((2, 1)\) is 1 right, 2 up. Clockwise quarter-turn: 2 right, 1 down, giving \((3, -2)\). ✓
  • \((4, 1)\) is 3 right, 2 up \(\to\) 2 right, 3 down: \((3, -4)\). \((4, 2)\) is 3 right, 3 up \(\to\) 3 right, 3 down: \((4, -4)\). ✓
  • (b) Undo the turn: rotation, \(90^\circ\) anticlockwise, about \((1, -1)\). ✓

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.