Mr. Vivek walks 6 meters North-east, then turns and walks 6 meters South-east, both at 60 degrees to east. He further moves 2 meters South and 4 meters West. What is the straight distance in meters between the point he started from and the point he finally reached? A. 2*sqrt(2) B. 2 C. sqrt(2) D. 1/sqrt(2)

GATE 2015 · General Aptitude · Direction Sense · medium

Answer: The straight-line distance is 2*sqrt(2) meters. Answer: A.

1. Decompose NE and SE segments: NE leg (60 deg above East): East = 6*cos(60) = 6*(1/2) = 3m, North = 6*sin(60) = 6*(sqrt(3)/2) = 3*sqrt(3)m. SE leg (60 deg below East): East = 6*cos(60) = 3m, North = -6*sin(60) = -3*sqrt(3)m.
2. Add remaining legs: From (6, 0): move 2m South => (6, -2). Then move 4m West => (6-4, -2) = (2, -2). Final position = (2, -2).
3. Compute straight-line distance from start: Start = (0, 0), End = (2, -2). d = sqrt(2^2 + (-2)^2) = sqrt(4 + 4) = sqrt(8) = 2*sqrt(2) meters.