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0580/31 May/Jun 2026, Question 9: Lines of Symmetry

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 3 marks

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The question, in short

On 4 by 4 grids with shaded squares, draw a line of symmetry, then shade one extra square to give one line of symmetry, and shade one extra square to give rotational symmetry of order 2.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Draw the line of symmetry on the 4 by 4 grid with the given shaded squares.

  1. 1Row 1 column 1 reflects to row 4 column 4, and row 2 column 1 to row 4 column 3
  2. 2Draw the diagonal line from the top right corner to the bottom left corner, across the full grid

AnswerThe diagonal from the top right corner to the bottom left corner of the grid

Part (aii) · 1 mark

Shade one more square on the grid so the pattern has exactly one line of symmetry.

  1. 1The shaded square in row 2 column 2 needs a mirror image
  2. 2Shade row 2 column 3 so the vertical centre line is the only line of symmetry
  3. 3(or shade row 3 column 2 for a horizontal line of symmetry)

AnswerShade row 2 column 3 (vertical line of symmetry) or row 3 column 2 (horizontal line of symmetry)

Part (b) · 1 mark

Shade one more square on the grid so the pattern has rotational symmetry of order 2.

  1. 1The corner squares already map onto each other under a half turn
  2. 2Row 2 column 2 maps to row 3 column 3 under a half turn about the centre
  3. 3Shade row 3 column 3

AnswerShade row 3 column 3

Stuck on a step? Read the free lesson: Lines of Symmetry

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Also searched as: 0580/31/M/J/26 · 0580_s26_qp_31 · 0580 s26 31 · question 9.
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