Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2021, Question 9: Rotation

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using the grid with triangle A at (2, 5), (3, 5), (3, 2) and triangle B at (−5, 7), (−4, 7), (−4, 4), carry out three transformations of A and identify the single transformation taking A to B.

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

Part (ai) · 2 marks

Draw where triangle A ends up after turning it 90° clockwise around the origin.

  1. 1Rotation 90° clockwise about O: (x, y) → (y, −x)
  2. 2(2, 5) → (5, −2), (3, 5) → (5, −3), (3, 2) → (2, −3)
  3. 3Draw the triangle (2, −3), (5, −3), (5, −2)

AnswerTriangle at (2, −3), (5, −3), (5, −2)

Part (aii) · 2 marks

Draw where triangle A ends up after mirroring it across the vertical line x = 5.

  1. 1Reflection in x = 5: (x, y) → (10 − x, y)
  2. 2(2, 5) → (8, 5), (3, 5) → (7, 5), (3, 2) → (7, 2)
  3. 3Draw the triangle (7, 2), (7, 5), (8, 5)

AnswerTriangle at (7, 2), (7, 5), (8, 5)

Part (aiii) · 2 marks

Draw where triangle A ends up after scaling it by factor 2 from centre (7, 7).

  1. 1From (7, 7), double each distance: (2, 5) → (7 − 10, 7 − 4) = (−3, 3)
  2. 2(3, 5) → (−1, 3), (3, 2) → (−1, −3)
  3. 3Draw the triangle (−3, 3), (−1, 3), (−1, −3)

AnswerTriangle at (−3, 3), (−1, 3), (−1, −3)

Part (b) · 2 marks

State fully the one transformation that carries triangle A onto triangle B.

  1. 1(2, 5) → (−5, 7): move 7 left and 2 up
  2. 2Translation by column vector (−7, 2)

AnswerTranslation, column vector (−7, 2)

Stuck on a step? Read the free lesson: Rotation

Practise more rotation 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 rotation

Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.