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0580/43 Oct/Nov 2024, Question 2: Negative Enlargement

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 12 marks

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The question, in short

Given points A(3, 7) and B(−1, 5), work out the midpoint of AB, the column vector for AB, and point C where AC = 3BA; then perform transformations on shape P on a grid.

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

Part (ai) · 2 marks

Work out the coordinates of the point halfway between A(3, 7) and B(−1, 5).

  1. 1x = (3 + (−1)) ÷ 2 = 1
  2. 2y = (7 + 5) ÷ 2 = 6
  3. 3Midpoint (1, 6)

Answer(1, 6)

Part (aii) · 1 mark

Express the displacement from A to B as a column vector.

  1. 1→AB = B − A = (−1 − 3, 5 − 7)
  2. 2= column vector (−4, −2)

Answercolumn vector (−4, −2)

Part (aiii) · 2 marks

Given AC = 3BA, work out the coordinates of point C.

  1. 1→BA = column vector (4, 2)
  2. 2→AC = 3→BA = column vector (12, 6)
  3. 3C = (3 + 12, 7 + 6) = (15, 13)

Answer(15, 13)

Part (bi) · 2 marks

Turn shape P by 180° around the point (4, 1) and draw the result.

  1. 1Each point (x, y) maps to (8 − x, 2 − y)
  2. 2(1, 1)→(7, 1), (4, 1)→(4, 1), (3, 3)→(5, −1), (1, 3)→(7, −1)
  3. 3Join (4, 1), (5, −1), (7, −1), (7, 1)

AnswerImage at (4, 1), (5, −1), (7, −1), (7, 1)

Part (bii) · 2 marks

Mirror shape P in the line y = x + 2 and draw the image.

  1. 1Draw the line y = x + 2 through (0, 2) and (1, 3)
  2. 2Each point (x, y) maps to (y − 2, x + 2)
  3. 3(1, 1)→(−1, 3), (4, 1)→(−1, 6), (3, 3)→(1, 5), (1, 3)→(1, 3)
  4. 4Join (1, 3), (−1, 3), (−1, 6), (1, 5)

AnswerImage at (1, 3), (−1, 3), (−1, 6), (1, 5)

Part (biii) · 3 marks

State fully the one transformation taking shape P onto shape Q.

  1. 1Q is inverted and half the size of P, so scale factor −1/2
  2. 2Lines joining (1, 1)→(4, 4) and (4, 1)→(2.5, 4) cross at (3, 3)
  3. 3Enlargement, centre (3, 3), scale factor −1/2

AnswerEnlargement, centre (3, 3), scale factor −1/2

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Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 2.
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