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0580/33 May/Jun 2022, Question 1: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Using coordinates on a 1 cm² grid, identify quadrilateral A, work out its area, and describe or draw transformations linking the quadrilaterals.

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

Part (a) · 1 mark

Give the correct geometric name for shape A.

  1. 1Sides: (−4, 5) to (−1, 4) = √10, (−1, 4) to (−4, 3) = √10
  2. 2(−4, 3) to (−5, 4) = √2, (−5, 4) to (−4, 5) = √2
  3. 3Two pairs of equal adjacent sides, so A is a kite

AnswerKite

Part (b) · 1 mark

Calculate the area of shape A in cm².

  1. 1Diagonals: from (−4, 5) to (−4, 3) = 2 cm, from (−5, 4) to (−1, 4) = 4 cm
  2. 2Area = 1/2 × 2 × 4 = 4 cm²

Answer4

Part (ci) · 3 marks

State the single transformation taking shape A to shape B, giving all details.

  1. 1B is twice the size of A (diagonals 4 and 8 instead of 2 and 4), so scale factor 2
  2. 2Join (−1, 4) to (6, 6) and (−4, 5) to (0, 8) and extend: the lines meet at (−8, 2)
  3. 3Check: (−8, 2) + 2 × ((−4, 5) − (−8, 2)) = (−8, 2) + (8, 6) = (0, 8)
  4. 4Enlargement, centre (−8, 2), scale factor 2

AnswerEnlargement, centre (−8, 2), scale factor 2

Part (cii) · 2 marks

State the single transformation taking shape A to shape C, giving all details.

  1. 1(−4, 5) → (−4, −5) and (−1, 4) → (−1, −6): each point moves 10 down
  2. 2Translation by column vector (0, −10)
  3. 3(Also accepted: reflection in y = −1, since (−4, 5) → (−4, −7) and (−4, 3) → (−4, −5))

AnswerTranslation column vector (0, −10) or Reflection in y = −1

Part (di) · 2 marks

Plot the image of shape C after turning it 90° anticlockwise about the origin.

  1. 1Rotation 90° anticlockwise about (0, 0): (x, y) → (−y, x)
  2. 2(−4, −5) → (5, −4), (−1, −6) → (6, −1)
  3. 3(−4, −7) → (7, −4), (−5, −6) → (6, −5)
  4. 4Plot (6, −1), (7, −4), (6, −5), (5, −4) and join them

AnswerCorrect rotation (6, −1), (7, −4), (6, −5), (5, −4)

Part (dii) · 2 marks

Plot the image of shape C after reflecting it in the line x = 1.

  1. 1Reflection in x = 1: (x, y) → (2 − x, y)
  2. 2(−4, −5) → (6, −5), (−1, −6) → (3, −6)
  3. 3(−4, −7) → (6, −7), (−5, −6) → (7, −6)
  4. 4Plot (3, −6), (6, −5), (7, −6), (6, −7) and join them

AnswerCorrect reflection (3, −6), (6, −5), (7, −6), (6, −7)

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Also searched as: 0580/33/M/J/22 · 0580_s22_qp_33 · 0580 s22 33 · question 1.
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