A travels 8 km from East to West and turns right and travel 2 km. Now again he turn right and travel 5 km. In which direction is he now positioned with reference to starting point?

Question

Accepted Answer

The correct option is 2:Detailed Explanation of Why Option 2 (North-West) is Correct

This is a classic directional reasoning problem that requires careful visualization or sketching of the path taken by the traveler, A. To solve this, we must precisely track the movement relative to the starting point and correctly interpret the direction of the "right turns" at each stage.

**Step 1: The Initial Movement**
The problem states that A travels 8 km from East to West. We typically represent East as moving right on a map and West as moving left. If A starts at point O (the origin), moving from East to West means moving 8 km horizontally to the left. Let's call the ending point of this first leg P.

**Step 2: The First Turn and Movement**
From point P, A turns right and travels 2 km. When a person is traveling West, a right turn places them facing North. Thus, A moves 2 km vertically upwards (North) from point P. Let's call this new point Q.

**Step 3: The Second Turn and Movement**
From point Q, A turns right again and travels 5 km. Since A was traveling North, a right turn means A now faces East. A travels 5 km horizontally to the right from point Q, ending up at the final position, R.

**Step 4: Determining the Final Position Relative to the Start (O)**
To find the final position (R) with reference to the starting point (O), we compare the net displacement in the East-West and North-South directions:  * **North-South displacement:** A moved 2 km North (upwards). The final position R is 2 km North of the starting point O.
  * **East-West displacement:** A initially moved 8 km West (left) and then moved 5 km East (right). The net horizontal movement is $8\text{ km (West)} - 5\text{ km (East)} = 3\text{ km West}$.Since the final position R is 2 km North and 3 km West of the starting point O, the current position is located in the **North-West** quadrant relative to the origin. Therefore, Option 2, North-West, is the correct direction.-----Analysis of Incorrect Options

The incorrect option is 1: South-West.
This option would imply that the final position is to the South and West of the starting point. However, A moved 2 km North and never traveled South, making a South component impossible.

The incorrect option is 3: North-East.
This option would imply that the final position is to the North and East of the starting point. While A is definitely North of the start, the net horizontal movement was $8\text{ km West}$ versus only $5\text{ km East}$. Since the Westward travel distance (8 km) was greater than the Eastward travel distance (5 km), the final position must be West of the starting point, not East.

The incorrect option is 4: South-East.
This option suggests the position is South and East of the starting point. This is incorrect because, as established, A's net North-South displacement is 2 km North, and the net East-West displacement is 3 km West. The path simply does not lead to the South-East quadrant.