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0580/23 May/Jun 2026, Question 12: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 9 marks

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The question, in short

Grid with triangles A, B and C; describe transformations mapping A to B and A to C, then draw images of A after a reflection and a translation.

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

Part (ai) · 3 marks

Describe fully the single transformation taking triangle A onto triangle B.

  1. 1A has vertices (1, −4), (2, −4), (2, −2); B has (4, 1), (4, 2), (2, 2)
  2. 2(x, y) → (−y, x) maps each vertex of A onto B
  3. 3Rotation 90° anticlockwise about (0, 0)

AnswerRotation, 90° anticlockwise, centre (0, 0)

Part (aii) · 3 marks

Describe fully the single transformation taking triangle A onto triangle C.

  1. 1C is twice the size of A and upside down, so scale factor −2
  2. 2Lines joining corresponding vertices, e.g. (2, −2) to (−4, −2) and (1, −4) to (−2, 2), meet at (0, −2)
  3. 3Enlargement, scale factor −2, centre (0, −2)

AnswerEnlargement, scale factor −2, centre (0, −2)

Part (bi) · 1 mark

Draw triangle A's image after reflection in the y-axis.

  1. 1Change the sign of each x-coordinate: (1, −4) → (−1, −4), (2, −4) → (−2, −4), (2, −2) → (−2, −2)
  2. 2Draw the triangle with these vertices

AnswerCorrect triangle at (−2, −2), (−2, −4), (−1, −4)

Part (bii) · 2 marks

Draw triangle A's image after translation by column vector (−1, 3).

  1. 1Move each vertex 1 left and 3 up
  2. 2(1, −4) → (0, −1), (2, −4) → (1, −1), (2, −2) → (1, 1)
  3. 3Draw the triangle with these vertices

AnswerCorrect triangle at (0, −1), (1, −1), (1, 1)

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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 12.
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