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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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.