Lemmara logoLemmaraWorked solution

0580/32 May/Jun 2021, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using four polygons drawn on a 1 cm² coordinate grid, identify the shaded shape, measure its area, describe three transformations, and draw a reflected image.

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

Part (a) · 1 mark

State the mathematical name of the shaded polygon.

  1. 1The shaded shape has 5 sides, so it is a pentagon

AnswerPentagon

Part (b) · 2 marks

Work out the area of the shaded polygon in cm².

  1. 1Vertices: (−2, 2), (−1, 4), (−2, 6), (−4, 6), (−6, 4)
  2. 2Surrounding rectangle from x = −6 to −1, y = 2 to 6: 5 × 4 = 20
  3. 3Corner triangles outside the shape: 1/2×1×2 + 1/2×1×2 + 1/2×2×2 + 1/2×4×2 = 8
  4. 4Area = 20 − 8 = 12

Answer12

Part (ci) · 2 marks

Describe fully the single transformation taking the shaded polygon to polygon A.

  1. 1Each vertex moves 7 right and 4 up, e.g. (−2, 2) → (5, 6)
  2. 2Translation by column vector (7, 4)

AnswerTranslation, column vector (7, 4)

Part (cii) · 3 marks

Describe fully the single transformation taking the shaded polygon to polygon B.

  1. 1Each point (x, y) maps to (−x, −y), e.g. (−2, 2) → (2, −2)
  2. 2Rotation, 180°, centre (0, 0)

AnswerRotation, centre (0, 0), 180°

Part (ciii) · 3 marks

Describe fully the single transformation taking the shaded polygon to polygon C.

  1. 1C is the same shape with sides half as long, so scale factor 0.5
  2. 2Lines joining matching vertices meet at (4, 2)
  3. 3Enlargement, centre (4, 2), scale factor 0.5

AnswerEnlargement, centre (4, 2), scale factor 0.5

Part (d) · 2 marks

Draw the shaded polygon's image after reflection in the line y = 0.

  1. 1Reflect in y = 0 (the x-axis): (x, y) → (x, −y)
  2. 2Plot (−2, −2), (−1, −4), (−2, −6), (−4, −6), (−6, −4) and join to make the pentagon

AnswerPentagon at (−2, −2), (−1, −4), (−2, −6), (−4, −6), (−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: 0580/32/M/J/21 · 0580_s21_qp_32 · 0580 s21 32 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.