4024/12 Oct/Nov 2024, Question 24: Perpendicular Lines
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Given points P(−1, 4) and Q(−3, −2), work out the midpoint of PQ and the equation of the line through P that is perpendicular to PQ.
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Part (a) · 1 mark
Work out the coordinates of the point halfway between P(−1, 4) and Q(−3, −2).
- 1Midpoint = ((−1 + (−3))/2, (4 + (−2))/2) = (−2, 1)
Answer(−2, 1)
Part (b) · 4 marks
Work out the equation of the straight line that goes through P(−1, 4) and is at right angles to PQ.
- 1Gradient PQ = (−2 − 4)/(−3 − (−1)) = −6/−2 = 3
- 2Perpendicular gradient = −1/3
- 3Through P(−1, 4): 4 = −1/3 × (−1) + c, so c = 4 − 1/3 = 11/3
- 4y = −1/3 x + 11/3
Answery = −1/3 x + 11/3
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Also searched as: 4024/12/O/N/24 · 4024_w24_qp_12 · 4024 w24 12 · question 24.
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