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Question 1 - NCERT Exemplar - MCQ - Chapter 7 Class 10 Coordinate Geometry (Term 1)

Last updated at Oct. 23, 2021 by

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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