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

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 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.