Lemmara logoLemmaraWorked solution

0580/12 May/Jun 2025, Question 16: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 11 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

On a 1 cm² grid with triangles A, B, C and point P, find areas, coordinates, a translated point, a reflected triangle, and describe transformations between triangles.

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

Part (a) · 1 mark

Find the area of triangle B using its vertices on the grid.

  1. 1Base 2, height 6: 1/2 × 2 × 6 = 6 cm²

Answer6

Part (bi) · 1 mark

Write down the coordinates of point P from the diagram.

  1. 1P = (4, −3)

Answer(4, −3)

Part (bii) · 1 mark

Find the coordinates of P after translation by the vector (−20, 12).

  1. 1(4 − 20, −3 + 12)
  2. 2= (−16, 9)

Answer(−16, 9)

Part (c) · 2 marks

Draw triangle A reflected in the line y = −1.

  1. 1Reflect in y = −1: y → −2 − y
  2. 2(1, 0) → (1, −2), (2, 0) → (2, −2), (2, 3) → (2, −5)
  3. 3Draw the triangle at (1, −2), (2, −2), (2, −5)

AnswerTriangle drawn with coordinates (1, −2 ) , (2, −2 ) and (2, −5)

Part (di) · 3 marks

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

  1. 1Base 1 → 2 and height 3 → 6: scale factor 2
  2. 2Centre = 2 × (1, 0) − (3, 0) = (−1, 0)
  3. 3Enlargement, scale factor 2, centre (−1, 0)

AnswerEnlargement, scale factor 2, centre (−1, 0)

Part (dii) · 3 marks

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

  1. 1The vertex (2, 3) stays fixed, so it is the centre
  2. 2Vertical side of A (down from (2, 3)) becomes horizontal side of C (left from (2, 3))
  3. 3Rotation, 90° clockwise, centre (2, 3)

AnswerRotation, 90° clockwise, centre (2, 3)

Stuck on a step? Read the free lesson: Describing Transformations

Practise more describing transformations questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on describing transformations

Also searched as: 0580/12/M/J/25 · 0580_s25_qp_12 · 0580 s25 12 · question 16.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.