4MA1/1H Jun 2019, Question 23: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Kite ABCD has AB = AD and CB = CD, with B at (10, 19) and D at (2, 7). Find the equation of line AC in the form py + qx = r with integer p, q, r.
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Solution · 5 marks
- 1(10 + 2) / 2 = 6
- 2(19 + 7) / 2 = 13
- 3midpoint of BD is (6, 13)
- 4(19 − 7) / (10 − 2) = 12 / 8 = 3/2
- 5gradient of BD is 3/2
- 6gradient of AC is −2/3 because perpendicular to BD
- 7using y = mx + c with m = −2/3 and point (6, 13)
- 813 = (−2/3)(6) + c
- 913 = −4 + c
- 10c = 17
- 11y = (−2/3)x + 17
- 12multiply through by 3: 3y = −2x + 51
- 133y + 2x = 51
Answer3y + 2x = 51
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