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0580/43 May/Jun 2022, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

On a grid, triangle T has vertices (−4, 3), (−4, 2) and (−1, 2); triangle A has vertices (1.5, 4.5), (6, 4.5) and (6, 3). Perform transformations and find an enlarged area.

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

Part (ai) · 2 marks

Plot and draw the mirror image of T across the line y = x.

  1. 1Reflection in y = x: (x, y) → (y, x)
  2. 2(−4, 3) → (3, −4), (−4, 2) → (2, −4), (−1, 2) → (2, −1)
  3. 3Draw the triangle at (2, −1), (2, −4), (3, −4)

AnswerTriangle drawn at (2, −1), (2, −4), (3, −4)

Part (aii) · 2 marks

Plot and draw T moved by the column vector (−1, 3).

  1. 1Add (−1, 3) to each vertex
  2. 2(−4, 3) → (−5, 6), (−4, 2) → (−5, 5), (−1, 2) → (−2, 5)
  3. 3Draw the triangle at (−5, 6), (−2, 5), (−5, 5)

AnswerTriangle drawn at (−5, 6), (−2, 5), (−5, 5)

Part (aiii) · 3 marks

State the single transformation taking T onto A, giving its type and full details.

  1. 1A is upside down and 1.5 times as big (side 3 → 4.5), so scale factor −1.5
  2. 2Centre (0, 3): (−4, 2) − (0, 3) = (−4, −1), × −1.5 = (6, 1.5), image (6, 4.5)
  3. 3(−1, 2): (−1, −1) × −1.5 = (1.5, 1.5), image (1.5, 4.5)
  4. 4Enlargement, scale factor −1.5, centre (0, 3)

AnswerEnlargement, scale factor −1.5, centre (0, 3)

Part (b) · 2 marks

Quadrilateral P has area 20 cm² and is enlarged by scale factor 1.2 to give Q; find Q's area.

  1. 1Area scale factor = 1.2² = 1.44
  2. 2Area of Q = 20 × 1.44 = 28.8 cm²

Answer28.8, 28 8/10, 28 4/5

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Also searched as: 0580/43/M/J/22 · 0580_s22_qp_43 · 0580 s22 43 · question 2.
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