4MA1/1H Nov 2021, Question 20: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 7 marks
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The question, in short
Find the area of triangle ABC, where L runs through A(−6, 2) and B(5, 3), M is perpendicular to L through the midpoint of AB, and M meets x = −1 at C.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 7 marks
- 1Gradient of L = (3 − 2)/(5 + 6) = 1/11, so gradient of M = −11
- 2Midpoint of AB = (−0.5, 2.5); M: y − 2.5 = −11(x + 0.5), so y = −11x − 3
- 3At x = −1, y = 11 − 3 = 8, so C = (−1, 8)
- 4AB = √122 and height from C to midpoint = √(0.5² + 5.5²) = √30.5
- 5Area = 1/2 × √122 × √30.5 = 1/2 × 61 = 30.5
Answer30.5
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