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0580/33 Oct/Nov 2022, Question 8: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 14 marks

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The question, in short

Grid transformations and vectors: reflect shape A, describe mappings A to B and A to C, compare areas, find vector AB, plot C, and calculate 3p and t − p.

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

Part (ai) · 2 marks

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

  1. 1Reflect in y = −1: (x, y) → (x, −2 − y)
  2. 2Draw shape at (−4, −3), (−3, −3), (−3, −4), (−4, −5)

AnswerShape drawn at (−4, −3), (−3, −3), (−4, −5), (−3, −4)

Part (aii) · 3 marks

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

  1. 1(−4, 1) → (4, −1), (−3, 2) → (3, −2): (x, y) → (−x, −y)
  2. 2Rotation, 180°, centre (0, 0)

AnswerRotation, 180°, centre (0, 0)

Part (aiii) · 3 marks

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

  1. 1Side 1 → 3, so scale factor 3
  2. 2Lines through (−4, 1) and (2, 3), and through (−3, 1) and (5, 3), meet at (−7, 0)
  3. 3Enlargement, scale factor 3, centre (−7, 0)

AnswerEnlargement, scale factor 3, centre (−7, 0)

Part (aiv) · 2 marks

Complete the statement giving how many times bigger the area of shape C is than shape A.

  1. 1Area A = 1/2 × (1 + 2) × 1 = 1.5
  2. 2Area C = 1/2 × (3 + 6) × 3 = 13.5
  3. 313.5 ÷ 1.5 = 9 (= 3²)

Answer9

Part (bi) · 1 mark

Write the vector AB as a column vector.

  1. 1AB = column vector (6 − 3, 6 − 2) = column vector (3, 4)

Answercolumn vector (3, 4)

Part (bii) · 1 mark

Given BC = column vector (4, −5), plot point C on the grid.

  1. 1C = (6 + 4, 6 − 5) = (10, 1)
  2. 2Plot C at (10, 1)

AnswerPoint C plotted at (10, 1)

Part (ci) · 1 mark

Work out 3p where p = column vector (5, −12).

  1. 13p = column vector (15, −36)

Answercolumn vector (15, −36)

Part (cii) · 1 mark

Work out t − p where t = column vector (4, 7).

  1. 1t − p = column vector (4 − 5, 7 − (−12)) = column vector (−1, 19)

Answercolumn vector (−1, 19)

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Also searched as: 0580/33/O/N/22 · 0580_w22_qp_33 · 0580 w22 33 · question 8.
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