4MA1/2HR Jan 2023, Question 25: Perpendicular Lines
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
Trapezium ABCD has AB parallel to DC, with A(−4, 6), B(2, 3), D(−1, 8) and one line of symmetry meeting CD at E. Find E's coordinates.
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Solution · 6 marks
- 1Midpoint of AB = ((−4 + 2)/2, (6 + 3)/2) = (−1, 4.5)
- 2Gradient AB = (3 − 6) ÷ (2 + 4) = −0.5, so the line of symmetry has gradient 2
- 3Line of symmetry through (−1, 4.5): y = 2x + 6.5
- 4CD is parallel to AB and passes through D(−1, 8): y = −0.5x + 7.5
- 52x + 6.5 = −0.5x + 7.5 gives x = 0.4 and y = 7.3, so E is (0.4, 7.3)
Answer(0.4, 7.3)
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