The fault line 3x + y – 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
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Last updated at Sept. 9, 2021 by Teachoo
Transcript
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)
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