0580/43 May/Jun 2026, Question 14: Perpendicular Lines
Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 7 marks
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The question, in short
Given points A (5, 2) and B (−3, 6), work out the distance between them and the equation of a line at right angles to AB through (−2, 5), in y = mx + c form.
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Part (a) · 3 marks
Work out the distance between the two given points A and B.
- 1Δx = −3 − 5 = −8, Δy = 6 − 2 = 4
- 2AB² = (−8)² + 4² = 80
- 3AB = √80 = 8.94
Answer8.94 or 8.944 to 8.945
Part (b) · 4 marks
Determine the equation, as y = mx + c, of the line at right angles to AB passing through (−2, 5).
- 1Gradient AB = (6 − 2)/(−3 − 5) = −1/2
- 2Perpendicular gradient = −1 ÷ (−1/2) = 2
- 35 = 2 × (−2) + c ⇒ c = 9
- 4y = 2x + 9
Answery = 2x + 9
Stuck on a step? Read the free lesson: Perpendicular Lines
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Also searched as: 0580/43/M/J/26 · 0580_s26_qp_43 · 0580 s26 43 · question 14.
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