WMA11/01 Jan 2025, Question 2: Perpendicular Lines
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks
The question, in short
Given points A(−2√3, 5) and B(7√3, 8) on line l₁, find the gradient in the form p√3, then find the equation of the perpendicular line l₂ through A.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Show, with full working, that the gradient of the line through A and B equals p√3 and find the rational value of p.
- 1Gradient = (8 − 5)/(7√3 − (−2√3)) = 3/(9√3)
- 2= 1/(3√3)
- 3Rationalise: 1/(3√3) × √3/√3 = √3/9
- 4So gradient = (1/9)√3, p = 1/9
AnswerShown: gradient = 3/(9√3) = √3/9, so p = 1/9
Part (b) · 3 marks
Find the equation of l₂, perpendicular to l₁ through A, in the form y = mx + c.
- 1Perpendicular gradient = −1 ÷ (√3/9) = −9/√3 = −3√3
- 2Through A(−2√3, 5): y − 5 = −3√3(x + 2√3)
- 3y − 5 = −3√3x − 18
- 4y = −3√3x − 13
Answery = −3√3x − 13
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