Point P divides the line segment joining R (−1, 3) and S (9, 8) in ratio k:1. If P lies on the line x – y + 2 = 0, then value of k is
(a) 2/3  (b) 1/2   (c) 1/3    (d) 1/4

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Transcript

Question 35 Point P divides the line segment joining R (βˆ’1, 3) and S (9, 8) in ratio k:1. If P lies on the line x – y + 2 = 0, then value of k is (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4 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— 9 + 1 Γ— (βˆ’1))/(π‘˜ + 1) x = (πŸ—π’Œ βˆ’ 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— 8 + 1 Γ— 3)/(π‘˜ + 1) y = (πŸ–π’Œ + πŸ‘)/(π’Œ + 𝟏) Since point P lies on line It will satisfy it’s equation Putting values of x and y in equation x βˆ’ y + 2 = 0 (πŸ—π’Œ βˆ’ 𝟏)/(π’Œ + 𝟏)βˆ’(πŸ–π’Œ + πŸ‘)/(π’Œ + 𝟏) + 2 = 0 ((9π‘˜ βˆ’1) βˆ’ (8π‘˜ + 3))/(π‘˜ + 1) + 2 = 0 (9π‘˜ βˆ’ 1 βˆ’ 8π‘˜ βˆ’ 3)/(π‘˜ + 1) + 2 = 0 (π‘˜ βˆ’ 4)/(π‘˜ + 1) + 2 = 0 (π‘˜ βˆ’ 4 + 2(π‘˜ + 1))/(π‘˜ + 1) = 0 (πŸ‘π’Œ βˆ’ 𝟐)/(π’Œ + 𝟏) = 0 3k βˆ’ 2 = 0 3k = 2 k = 𝟐/πŸ‘ So, the correct answer is (a)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.