4MA1/1H Jan 2023, Question 23: The Perpendicular Bisector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
Kite ABCD has AB = AD and CB = CD, with B = (k, 1), D = (8, 7). Line BD is parallel to 5y − 3x = 6. Find an equation of AC in the form px + qy = r, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 15y − 3x = 6 gives y = (3/5)x + 6/5, so BD has gradient 3/5
- 2Gradient BD = (7 − 1)/(8 − k) = 3/5, so 8 − k = 10 and k = −2
- 3Midpoint of BD = ((−2 + 8)/2, (1 + 7)/2) = (3, 4); AC passes through it
- 4Kite diagonals are perpendicular, so gradient of AC = −5/3
- 5y − 4 = −5/3 (x − 3), so 3y − 12 = −5x + 15, giving 5x + 3y = 27
Answer5x + 3y = 27
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