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0580/41 May/Jun 2024, Question 2: Area Factor of Similar Shapes

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 8 marks

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The question, in short

On a grid, transform shaded triangle T with vertices (1, −3), (2, −1), (5, −3) by reflection, translation and enlargement, then find the area of shape R after two successive enlargements.

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

Part (ai) · 1 mark

Draw the image of triangle T after reflection in the x-axis.

  1. 1Reflection in the x-axis: (x, y) → (x, −y)
  2. 2(1, −3) → (1, 3), (2, −1) → (2, 1), (5, −3) → (5, 3)
  3. 3Draw the triangle at (2, 1), (1, 3), (5, 3)

AnswerTriangle at (2, 1) (1, 3) (5, 3)

Part (aii) · 2 marks

Draw the image of triangle T after translation by column vector (−5, −2).

  1. 1Add (−5, −2) to each vertex
  2. 2(1, −3) → (−4, −5), (2, −1) → (−3, −3), (5, −3) → (0, −5)
  3. 3Draw the triangle at (−4, −5), (−3, −3), (0, −5)

AnswerTriangle at (−4, −5) (−3, −3) (0, −5)

Part (aiii) · 2 marks

Draw the image of triangle T after enlargement by scale factor −1/2 with centre (−1, 1).

  1. 1From centre (−1, 1), multiply each vector by −1/2
  2. 2(1, −3): vector (2, −4) → (−1, 2), image (−2, 3)
  3. 3(2, −1): vector (3, −2) → (−1.5, 1), image (−2.5, 2)
  4. 4(5, −3): vector (6, −4) → (−3, 2), image (−4, 3)
  5. 5Draw the triangle at (−2.5, 2), (−4, 3), (−2, 3)

AnswerTriangle at (−2.5, 2) (−4, 3) (−2, 3)

Part (b) · 3 marks

Shape P area 10 cm² is enlarged by scale factor 3 to Q, then Q by 2/5 to R; calculate area of R.

  1. 1Area scale factor = 3² × (2/5)² = 9 × 4/25 = 36/25
  2. 2Area of R = 10 × 36/25 = 14.4 cm²

Answer14.4

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Also searched as: 0580/41/M/J/24 · 0580_s24_qp_41 · 0580 s24 41 · question 2.
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