4MA1/1H Jun 2018, Question 20: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Isosceles triangle ABC has AB = AC, A at (4, 37), and B, C on 3y = 2x + 12. Find the symmetry line's equation as px + qy = r with integer coefficients, showing working.
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Solution · 5 marks
- 13y = 2x + 12 gives y = (2/3)x + 4, so BC has gradient 2/3
- 2The line of symmetry is perpendicular to BC, so its gradient is −3/2
- 3It passes through A(4, 37): y − 37 = −3/2 (x − 4)
- 4Multiply by 2: 2y − 74 = −3x + 12, so 3x + 2y = 86
Answer3x + 2y = 86
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