4MA1/1H Jun 2025, Question 25: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
PQRS is a square with diagonal PR, P(4, 7) and R(8, −5). Find the equation of the line through Q and S in the form ay = bx + c with integer coefficients.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Midpoint of PR = ((4 + 8)/2, (7 + (−5))/2) = (6, 1)
- 2Gradient of PR = (−5 − 7)/(8 − 4) = −3
- 3QS is perpendicular to PR: gradient 1/3
- 4y − 1 = 1/3 (x − 6), so y = x/3 − 1
- 53y = x − 3
Answer3y = x − 3
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