X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km?
Options:
(A) 1
(B) √2
(C) √3
(D) 2
Official Answer Key:
C
Step-by-Step Solution & Explanation
Taking Z = (0, 0) and using unit vectors (with NE/SE at 45° to the axes, magnitude 1 km each):
Y = Z + (SE) = (sin45°, −cos45°) = (0.7071, −0.7071)
X = Y + (NE) = Y + (0.7071, 0.7071) = (1.4142, 0)
W = Z + (−1, 0) = (−1, 0)
P = W + (0, −1) = (−1, −1)
Q = P + (1, 0) = (0, −1)
Distance XQ = √[(1.4142−0)² + (0−(−1))²] = √[2 + 1] = √3 km. Answer: (C).
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