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0580/42 May/Jun 2024, Question 10: Length of a Line Segment

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Work with points A(6, 2) and B(3, −4) and the line 4x + 3y − 12 = 0: locate a midpoint, measure a distance, and derive gradient, intercept and a perpendicular line.

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Part (ai) · 2 marks

Determine the coordinates halfway between A and B.

  1. 1Midpoint = ((6 + 3)/2, (2 + (−4))/2)
  2. 2= (4.5, −1)

Answer(4.5, −1)

Part (aii) · 3 marks

Work out how far apart A and B are.

  1. 1AB² = (6 − 3)² + (2 − (−4))² = 9 + 36 = 45
  2. 2AB = √45 = 6.708… ≈ 6.71

Answer6.71 or 6.708...

Part (bi) · 2 marks

Determine the slope of the given line l.

  1. 13y = −4x + 12
  2. 2y = −4/3 x + 4
  3. 3Gradient = −4/3

Answer−4/3

Part (bii) · 2 marks

State where line l meets the y-axis, giving coordinates.

  1. 1x = 0: 3y = 12, y = 4
  2. 2(0, 4)

Answer(0, 4)

Part (biii) · 3 marks

For line p through (6, 5) at right angles to l, express its equation as y = mx + c.

  1. 1Perpendicular gradient = −1 ÷ (−4/3) = 3/4
  2. 25 = 3/4 × 6 + c, so c = 5 − 4.5 = 0.5
  3. 3y = (3/4)x + 1/2

Answery = (3/4)x + 1/2

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 10.
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