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0580/12 Oct/Nov 2025, Question 19: Reflection

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 6 marks

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The question, in short

Using the grid with flags F and A, perform two transformations of flag F and identify the single transformation taking F to A.

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

Part (a) · 2 marks

Draw flag F reflected in the vertical line x = −1.

  1. 1Mirror line is x = −1. Each y stays the same.
  2. 2x = 2 is 3 right of the line, so it goes 3 left: x = −4
  3. 3x = 3 is 4 right of the line, so it goes 4 left: x = −5
  4. 4Draw pole (−4, 2) to (−4, 5) and flag square (−4, 4), (−5, 4), (−5, 5), (−4, 5)

AnswerFully correct reflection, points (−4, 5) (−5, 5) (−4, 4) (−5, 4) (−4, 2)

Part (b) · 2 marks

Draw flag F rotated 180° about the origin (0, 0).

  1. 1Rotate 180° about (0, 0): (x, y) → (−x, −y)
  2. 2Draw pole (−2, −2) to (−2, −5) and flag square (−2, −4), (−3, −4), (−3, −5), (−2, −5)

AnswerFully correct rotation, points (−2, −2) (−2, −4) (−2, −5) (−3, −5) (−3, −4)

Part (c) · 2 marks

Describe fully the single transformation mapping flag F onto flag A.

  1. 1Pole base (2, 2) → (4, −4): move 2 right and 6 down
  2. 2Translation by column vector (2, −6)

AnswerTranslation column vector (2, −6)

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Also searched as: 0580/12/O/N/25 · 0580_w25_qp_12 · 0580 w25 12 · question 19.
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