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
CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
Last updated at April 16, 2024 by Teachoo
Question 35 Point P divides the line segment joining R (β1, 3) and S (9, 8) in ratio k:1. If P lies on the line x β y + 2 = 0, then value of k is (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4 Using section formula x = (ππ ππ + ππ ππ)/(ππ + ππ) x = (π Γ 9 + 1 Γ (β1))/(π + 1) x = (ππ β π)/(π + π) y = (ππ ππ + ππ ππ)/(ππ + ππ) y = (π Γ 8 + 1 Γ 3)/(π + 1) y = (ππ + π)/(π + π) Since point P lies on line It will satisfy itβs equation Putting values of x and y in equation x β y + 2 = 0 (ππ β π)/(π + π)β(ππ + π)/(π + π) + 2 = 0 ((9π β1) β (8π + 3))/(π + 1) + 2 = 0 (9π β 1 β 8π β 3)/(π + 1) + 2 = 0 (π β 4)/(π + 1) + 2 = 0 (π β 4 + 2(π + 1))/(π + 1) = 0 (ππ β π)/(π + π) = 0 3k β 2 = 0 3k = 2 k = π/π So, the correct answer is (a)