What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?

(a) (1, 0)   (b) (0, 1)   (c) (−2, 1)   (d) (−1, 0)  

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  1. Class 10
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Question 49 What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear? (a) (1, 0) (b) (0, 1) (c) (−2, 1) (d) (−1, 0) Let required point be Q (x, y) Given that Distance of Q from K is twice distance from E ∴ QK = 2 × QE Also, since K, Q and E are collinear KQ : QE = 2: 1 Coordinates of Q = ((𝑚_1 𝑥_2 + 𝑚_2 𝑥_1)/(𝑚_1 + 𝑚_2 ), (𝑚_1 𝑦_2 + 𝑚_2 𝑦_1)/(𝑚_1 + 𝑚_2 )) = ((2 × 2 + 1 × (−4) )/(2 + 1), (2 × 1 + 1 × 1)/(2 + 1)) = ((4 − 4)/3, (2 + 1)/3) = (0/3, 3/3) = (0, 1) So, the correct answer is (b)

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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.