4024/11 May/Jun 2024, Question 23: Perpendicular Lines
Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 7 marks
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The question, in short
For segment AB with A(−2, 5) and B(1, 3): find point C given B is midpoint of AC, find t where AB = √t, and find the perpendicular line through A in y = mx + c form.
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Part (a) · 1 mark
Find the coordinates of point C, given that B is the midpoint of segment AC.
- 1C = (2 × 1 − (−2), 2 × 3 − 5)
- 2C = (4, 1)
Answer(4, 1)
Part (b) · 2 marks
Find the value of t, given that the length of AB equals √t.
- 1AB² = (−2 − 1)² + (5 − 3)² = 9 + 4 = 13
- 2AB = √13, so t = 13
Answer13
Part (c) · 4 marks
Find the equation, in y = mx + c form, of the line through A perpendicular to AB.
- 1Gradient of AB = (3 − 5)/(1 − (−2)) = −2/3
- 2Perpendicular gradient = 3/2
- 3y − 5 = 3/2 (x − (−2))
- 4y = (3/2)x + 3 + 5
- 5y = (3/2)x + 8
Answery = (3/2)x + 8
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Also searched as: 4024/11/M/J/24 · 4024_s24_qp_11 · 4024 s24 11 · question 23.
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