Step 1: Understanding the Concept:
Direction sense problems involve tracking spatial displacement on a coordinate plane.
Standard directions are: North (Up), South (Down), East (Right), and West (Left).
A "right turn" while facing North leads to East. A "right turn" while facing East leads to South.
Step 2: Key Formula or Approach:
We should map the movements sequentially to visualize the geometric path created.
Displacement is the straight-line distance from the start point to the end point.
Step 3: Detailed Explanation:
Let's track the journey step-by-step from the origin (Point O):
1. Segment 1: Starting at point O, the person walks 12 km North to reach Point A. The distance OA is 12 km.
2. Segment 2: At Point A, the person turns right (East) and walks 5 km to reach Point B. The distance AB is 5 km.
3. Segment 3: At Point B, the person turns right again. Since they were facing East, a right turn means they are now heading South. They walk 12 km to reach Point C. The distance BC is 12 km.
Visualization:
The path forms three sides of a rectangle OABC.
The segment OA is 12 km North.
The segment BC is 12 km South.
Since North and South are exact opposite directions and the lengths are identical (12 km), the person has returned to the same horizontal latitude as the starting point.
In a rectangle, opposite sides are equal. Therefore, the distance from Point O to Point C (OC) must be equal to the distance from Point A to Point B (AB).
\[ OC = AB = 5 \text{ km} \]
The final position (C) is exactly 5 km East of the starting position (O).
Step 4: Final Answer:
He is 5 km far from the starting point.