0580/42 May/Jun 2025, Question 25: The Perpendicular Bisector
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 5 marks
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The question, in short
Given points P (8, 0) and Q (20, 6), determine the line that cuts PQ at right angles through its midpoint, giving it as y = mx + c.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Midpoint of PQ = ((8 + 20)/2, (0 + 6)/2) = (14, 3)
- 2Gradient of PQ = (6 − 0)/(20 − 8) = 1/2
- 3Perpendicular gradient = −2
- 43 = −2 × 14 + c, so c = 31
- 5y = −2x + 31
Answery = −2x + 31
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Also searched as: 0580/42/M/J/25 · 0580_s25_qp_42 · 0580 s25 42 · question 25.
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