Study the following information carefully and answer the given questions. Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a specific direction, and covers a certain distance before reaching its final position which is named as ship's captain's name. Movements of the ships: I. Ship A, steered by Captain P, starts moving north and covers 5m, then turns left and moves 8m, finally turning right and moving 10m to reach its final position. II. Ship B, steered by Captain Q, moves east for 12m, then turns right and moves 7m, finally turning right again and moving 3m to its final position. III. Ship C, steered by Captain R, starts by moving south for 6m, then turns right and moves 5m, then turns left and moves 9m to its final position. IV. Ship D, steered by Captain S, moves west for 10m, then turns left and moves 4m, finally turning right and moving 6m to its final position. V. Ship E, steered by Captain T, starts moving north for 8m, then turns right and moves 10m, finally turning right again and moving 5m to its final position. In which direction is S with respect to R in the final position?

### Concept & Direction Sense To find the relative direction, determine the final coordinates of each point on a Cartesian plane where the starting dock is the origin (0,0). North is positive y-axis, South is negative y-axis, East is positive x-axis, West is negative x-axis. ### Step-by-Step Solution * **Coordinate mapping for R:** Ship C moves south 6m $(0, -6)$, turns right (west) and moves 5m $(-5, -6)$, turns left (south) and moves 9m $(-5, -15)$. Final position $R = (-5, -15)$. * **Coordinate mapping for S:** Ship D moves west 10m $(-10, 0)$, turns left (south) and moves 4m $(-10, -4)$, turns right (west) and moves 6m $(-16, -4)$. Final position $S = (-16, -4)$. * **Determine relative direction:** To go from R to S, we move from x = -5 to x = -16 (West) and from y = -15 to y = -4 (North). * Since the movement is towards the North and West, S is North-West of R. ### Exam Strategy & Shortcut Instead of drawing the entire complex diagram for all ships, only trace the paths of the specific ships mentioned in the question to save time. ### Common Pitfall Misinterpreting left and right turns when moving South or West. Remember to orient yourself in the direction of travel. ### Final Answer Therefore, the correct answer is **North-west**.