Kundan moved 3 km in the West. Then he turned to his left and moved 4 km.…

In direction-sense problems, plot each movement on a coordinate grid with the start as the origin, North along +y and East along +x. A right turn rotates the current facing direction clockwise (North to East to South to West to North) and a left turn rotates it anticlockwise (North to West to South to East to North). Once every leg is plotted, the net displacement from the origin is the square root of (x squared plus y squared), and the direction is read from the sign of the final (x, y) coordinates -- which quadrant the point falls in.

1. Start at the origin (0, 0) facing West and move 3 km West, reaching (-3, 0).

2. Facing West, a left turn points South; moving 4 km South reaches (-3, -4).

3. Facing South, a right turn points West; moving 2 km West reaches (-5, -4).

4. Facing West, a right turn points North; moving 9 km North reaches (-5, 5).

The final point (-5, 5) has a negative x-coordinate and a positive y-coordinate, so it lies to the North-West of the origin. The straight-line distance is the square root of ((-5)2 + 52) = square root of 50 = 5 root 2 km, confirming 5 root 2 km, North-West as the answer.