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0580/42 Feb/Mar 2023, Question 6: Length of a Line Segment

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Using points A (0, 4) and B (8, 0), with L₁ horizontal through A and L₂ through A and B, find line equations and a perpendicular line through C (2, 3), then a length.

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

Part (a) · 1 mark

State the equation of the horizontal line L₁ passing through A.

  1. 1L₁ is horizontal through A(0, 4)
  2. 2y = 4

Answery = 4

Part (b) · 2 marks

Find the equation of L₂ through A and B in y = mx + c form.

  1. 1Gradient = (0 − 4)/(8 − 0) = −1/2
  2. 2y-intercept = 4
  3. 3y = −1/2 x + 4

Answery = −1/2 x + 4

Part (ci) · 3 marks

For L₃ through C (2, 3) perpendicular to L₂, show its equation is y = 2x − 1.

  1. 1Gradient of L₂ = −1/2, so perpendicular gradient = 2 (because 2 × −1/2 = −1)
  2. 2y = 2x + c through C(2, 3): 3 = 2 × 2 + c
  3. 3c = −1
  4. 4y = 2x − 1

Answery = 2x − 1

Part (cii) · 5 marks

Given L₃ meets the x-axis at D, calculate the length CD.

  1. 1At D, y = 0: 2x − 1 = 0, x = 1/2, so D = (1/2, 0)
  2. 2CD² = (2 − 1/2)² + (3 − 0)² = 2.25 + 9 = 11.25
  3. 3CD = √11.25 = 3.354… ≈ 3.35

Answer3.35 or 3.354...

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Also searched as: 0580/42/F/M/23 · 0580_m23_qp_42 · 0580 m23 42 · question 6.
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