4MA1/2HR Jan 2022, Question 22: Perpendicular Lines
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
Triangle ABC has a right angle at B, with A (p, 10), B (−1, −5), C (8, q) and gradient of AC equal to −6/7. Find p and q.
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Solution · 5 marks
- 1Gradient AB = 15/(p + 1) and gradient BC = (q + 5)/9
- 2Angle ABC = 90°, so product = −1: 15(q + 5) = −9(p + 1), giving 9p + 15q = −84
- 3Gradient AC: (10 − q)/(p − 8) = −6/7, giving 6p − 7q = −22
- 4Solve together (×7 and ×15, then add): 153p = −918, so p = −6
- 56 × (−6) − 7q = −22 gives q = −2, so p = −6, q = −2
Answerp = −6, q = −2
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