Question 43 The fault line 3x + y β 9 = 0 divides the line joining the Country P(1, 3) and Country Q(2, 7) internally in the ratio (a) 3 : 4 (b) 3 : 2 (c) 2 : 3 (d) 4 : 3
Using section formula
x = (ππ ππ + ππ ππ)/(ππ + ππ)
x = (π Γ 2 + 1 Γ 1)/(π + 1)
x = (ππ + π)/(π + π)
y = (ππ ππ + ππ ππ)/(ππ + ππ)
y = (π Γ 7 + 1 Γ 3)/(π + 1)
y = (ππ + π)/(π + π)
Since point Z lies on line
It will satisfy itβs equation
Putting values of x and y in equation
3x + y β 9 = 0
π((ππ+ π)/(π + π))+(ππ + π)/(π + π) β 9 = 0
(3(2π+ 1))/(π + 1)+(7π + 3)/(π + 1) β 9 = 0
(6π + 3)/(π + 1)+(7π + 3)/(π + 1) β 9 = 0
(6π + 3 + 7π + 3)/(π + 1) β 9 = 0
(13π + 6)/(π + 1) β 9 = 0
(13π + 6 β 9(π + 1))/(π + 1) = 0
(13π + 6 β 9π β 9)/(π + 1) = 0
(ππ β π)/(π + π) = 0
4k β 3 = 0
4k = 3
k = π/π
β΄ Required ratio is 3 : 4
So, the correct answer is (a)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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