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4MA1/2HR Jun 2020, Question 23: The Perpendicular Bisector

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks

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The question, in short

Points P(−1, 6) and Q(5, −4) are given. Find the perpendicular bisector of PQ as ax + by + c = 0 with integer coefficients.

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

Solution · 6 marks

  1. 1(−1 + 5)/2 = 2, (6 + (−4))/2 = 1, so midpoint is (2, 1)
  2. 2(−4 − 6)/(5 − (−1)) = (−10)/6 = −5/3, so gradient of PQ is −5/3
  3. 3perpendicular gradient is the negative reciprocal, so 3/5
  4. 4using point (2, 1) and y = (3/5)x + c: 1 = (3/5)(2) + c
  5. 51 = 6/5 + c, so c = 1 − 6/5 = −1/5
  6. 6y = (3/5)x − 1/5
  7. 7multiply through by 5: 5y = 3x − 1
  8. 8rearrange to 3x − 5y − 1 = 0

Answer3x − 5y − 1 = 0

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