If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

(A) –2  

(B) 2  

(C) –1  

(D) 1

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Question 1 If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is (A) –2 (B) 2 (C) –1 (D) 1 Given Distance between (2, −2) and (−1, x) = 5 √(( −1 −2)2+(𝑥−(−2))2) = 5 √(( −3)2+(𝑥+2)2) = 5 √(9+𝑥^2+2^2+4𝑥) = 5 √(9+𝑥^2+4+4𝑥) = 5 √(𝑥^2+4𝑥+13) = 5 Squaring both sides (√(𝑥^2+4𝑥+13))^2 = 52 x2 + 4x + 13 = 25 x2 + 4x + 13 − 25 = 0 x2 + 4x − 12 = 0 Solving by splitting the middle term x2 + 6x − 2x − 12 = 0 x(x + 6) − 2(x + 6) = 0 (x − 2) (x + 6) = 0 ∴ x = 2, −6 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.