Lemmara logoLemmaraWorked solution

0580/31 May/Jun 2023, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Name a four-sided polygon, then describe the single transformations mapping a shaded shape onto shapes A and B, and draw two images of the shaded shape on the grid.

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

Part (a) · 1 mark

Give the mathematical name for any polygon that has 4 sides.

  1. 1A polygon with 4 sides is a quadrilateral

AnswerQuadrilateral

Part (bi) · 3 marks

Describe fully the single transformation that maps the shaded shape onto shape A.

  1. 1(−6, 2) → (2, 6), (−5, 6) → (6, 5), (−2, 4) → (4, 2), (−2, 1) → (1, 2)
  2. 2Each point (x, y) → (y, −x), which is a quarter turn clockwise about the origin
  3. 3Rotation, 90° clockwise, centre (0, 0)

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

Part (bii) · 3 marks

Describe fully the single transformation that maps the shaded shape onto shape B.

  1. 1Shape B is smaller: side (−2, 4) to (−2, 1) has length 3, image side (2.5, −2) to (2.5, −3.5) has length 1.5
  2. 2Scale factor = 1.5 ÷ 3 = 1/2
  3. 3Lines through corresponding points, e.g. (−2, 1) to (2.5, −3.5) and (−6, 2) to (0.5, −3), meet at (7, −8)
  4. 4Enlargement, scale factor 1/2, centre (7, −8)

AnswerEnlargement, scale factor 1/2, centre (7, −8)

Part (ci) · 2 marks

Draw the image of the shaded shape after translation by the column vector (9, −6).

  1. 1Move each vertex 9 right and 6 down
  2. 2(−6, 2) → (3, −4), (−5, 6) → (4, 0), (−2, 4) → (7, −2), (−2, 1) → (7, −5)
  3. 3Join (4, 0), (7, −2), (7, −5), (3, −4)

AnswerCorrect translation (4, 0), (7, −2), (7, −5), (3, −4)

Part (cii) · 2 marks

Draw the image of the shaded shape after reflection in the line y = −1.

  1. 1Draw the line y = −1; each point keeps its x and goes the same distance to the other side
  2. 2(−2, 1) → (−2, −3), (−2, 4) → (−2, −6), (−5, 6) → (−5, −8), (−6, 2) → (−6, −4)
  3. 3Join (−2, −3), (−2, −6), (−5, −8), (−6, −4)

AnswerCorrect reflection (−2, −3), (−2, −6), (−5, −8), (−6, −4)

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: 0580/31/M/J/23 · 0580_s23_qp_31 · 0580 s23 31 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.