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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Question 43 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 Using section formula x = (π’ŽπŸ π’™πŸ + π’ŽπŸ π’™πŸ)/(π’ŽπŸ + π’ŽπŸ) x = (π‘˜ Γ— 2 + 1 Γ— 1)/(π‘˜ + 1) x = (πŸπ’Œ + 𝟏)/(π’Œ + 𝟏) y = (π’ŽπŸ π’šπŸ + π’ŽπŸ π’šπŸ)/(π’ŽπŸ + π’ŽπŸ) y = (π‘˜ Γ— 7 + 1 Γ— 3)/(π‘˜ + 1) y = (πŸ•π’Œ + πŸ‘)/(π’Œ + 𝟏) Since point Z lies on line It will satisfy it’s equation Putting values of x and y in equation 3x + y βˆ’ 9 = 0 πŸ‘((πŸπ’Œ+ 𝟏)/(π’Œ + 𝟏))+(πŸ•π’Œ + πŸ‘)/(π’Œ + 𝟏) βˆ’ 9 = 0 (3(2π‘˜+ 1))/(π‘˜ + 1)+(7π‘˜ + 3)/(π‘˜ + 1) βˆ’ 9 = 0 (6π‘˜ + 3)/(π‘˜ + 1)+(7π‘˜ + 3)/(π‘˜ + 1) βˆ’ 9 = 0 (6π‘˜ + 3 + 7π‘˜ + 3)/(π‘˜ + 1) βˆ’ 9 = 0 (13π‘˜ + 6)/(π‘˜ + 1) βˆ’ 9 = 0 (13π‘˜ + 6 βˆ’ 9(π‘˜ + 1))/(π‘˜ + 1) = 0 (13π‘˜ + 6 βˆ’ 9π‘˜ βˆ’ 9)/(π‘˜ + 1) = 0 (πŸ’π’Œ βˆ’ πŸ‘)/(π’Œ + 𝟏) = 0 4k βˆ’ 3 = 0 4k = 3 k = πŸ‘/πŸ’ ∴ Required ratio is 3 : 4 So, the correct answer is (a)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.