Question

A policeman left his police post and proceeded south $4\text{ km}$ on hearing a loud sound from point A. On reaching the place, he heard another sound and proceeded $4\text{ km}$ to his left to the point B. From B he proceeded left to reach another place C, $4\text{ km}$ away. In which direction he has to go to reach his police post?

• A. North
• B. South
• C. East
• D. West

Hint:

Draw a simple square outline as you trace the path: Down 4, Right 4, Up 4. This creates three sides of a perfect square. You are now standing to the right of your starting point, so you must look and walk West to get back home.

Answer 1

The Correct Option is D

Concept: Direction sense problems are resolved by plotting movements step-by-step onto a standard two-dimensional Cartesian plane, tracking changes in position relative to the cardinal directions: North (Up), South (Down), East (Right), and West (Left).

Step 1: Tracking the first movement to point A.
* Let the starting point, the police post, be located at the origin coordinates: $(0, 0)$. * The policeman travels South for $4\text{ km}$ to reach point A. * Moving South means moving down along the vertical y-axis. The coordinates of point A become: \[ A = (0, -4) \]

Step 2: Tracking the second movement to point B.
* From point A, the policeman turns to his left and travels $4\text{ km}$ to reach point B. * Because the policeman was facing South (downward), turning to "his left" means turning toward the East (to the right on our map). * Moving East adds distance along the horizontal x-axis. The coordinates of point B become: \[ B = (0 + 4, -4) = (4, -4) \]

Step 3: Tracking the third movement to point C.
* From point B, the policeman turns left again and travels $4\text{ km}$ to reach point C. * Since he was moving East, a left turn points him back toward the North (upward on our map). * Moving North adds distance along the vertical y-axis. The coordinates of point C become: \[ C = (4, -4 + 4) = (4, 0) \]

Step 4: Determining the final return direction.
* Let us compare the final position, point C $(4, 0)$, with the original police post position at $(0, 0)$. * Point C lies exactly on the positive x-axis, meaning it is exactly $4\text{ km}$ East of the police post. * To return to the police post $(0, 0)$ from point C $(4, 0)$, the policeman must travel directly along the negative horizontal axis, which means heading straight West. Thus, the correct direction is West, matching Option (D).