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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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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.