4MA1/1HR Jan 2021, Question 22: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Triangle ABC is isosceles with AB = AC; B(−1, 5), C(2, 10), M is midpoint of BC. Find the equation of line AM in the form py + qx = r with integer p, q, r.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Midpoint M = ((−1 + 2)/2, (5 + 10)/2) = (0.5, 7.5)
- 2Gradient of BC = (10 − 5) ÷ (2 − (−1)) = 5/3
- 3AM is perpendicular to BC (isosceles triangle), so its gradient is −3/5
- 4y − 7.5 = −3/5 (x − 0.5), so y = −3/5 x + 7.8
- 5Multiply by 5 and rearrange: 5y + 3x = 39
Answer5y + 3x = 39
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