4MA1/2HR Jun 2025, Question 24: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Line PQ on a 1 cm per unit grid has P(−5, a) and Q(7, 3a), a > 0, with PQ = 4√10 cm. Find the perpendicular bisector of PQ as y = mx + c with integer m and c.
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Solution · 6 marks
- 1PQ² = 12² + (2a)² = 144 + 4a² = 160, so a = 2
- 2P(−5, 2), Q(7, 6): gradient of PQ = 4/12 = 1/3
- 3Perpendicular gradient = −3; midpoint of PQ = (1, 4)
- 44 = −3 × 1 + c, so c = 7
- 5y = −3x + 7
Answery = −3x + 7
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