4024/12 May/Jun 2020, Question 24: Perpendicular Lines
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Point P is (h, 7) and lies on the line 3y + 2x = 5. Find h, then find the equation of line L, which is perpendicular to this line and passes through P.
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Part (a) · 2 marks
Find the value of h given that P (h, 7) lies on the line 3y + 2x = 5.
- 13 × 7 + 2h = 5
- 221 + 2h = 5
- 32h = −16, h = −8
Answer−8
Part (b) · 4 marks
Find the equation of line L, which is perpendicular to 3y + 2x = 5 and passes through P.
- 13y = −2x + 5, so y = −(2/3)x + 5/3: gradient −2/3
- 2Perpendicular gradient = −1 ÷ (−2/3) = 3/2
- 3From part (a), h = −8, so P is (−8, 7)
- 4Substitute P into y = (3/2)x + c: 7 = −12 + c, so c = 19
- 5y = (3/2)x + 19
Answery = (3/2)x + 19
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Also searched as: 4024/12/M/J/20 · 4024_s20_qp_12 · 4024 s20 12 · question 24.
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