Question

A person walks 12 km towards North, then turns right and walks 5 km. He again turns right and walks 12 km. How far is he from the starting point?

• A. 5 km
• B. 7 km
• C. 12 km
• D. 17 km

Hint:

Whenever you see a directional sequence that goes North $\rightarrow$ Right (East) $\rightarrow$ Right (South) where the first and third legs are exactly equal in length, the movements cancel each other out completely along the vertical axis. The net distance from start is simply equal to the middle horizontal step value—which is 5 km!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Direction sense problems track positional displacement using a standard two-dimensional map coordinates layout where North is oriented upwards, South is downwards, East is to the right, and West is to the left. By mapping the sequential movements step-by-step, we can trace a closed geometric shape to evaluate the final shortest straight-line distance separating the person's final coordinate from the initial starting origin.

Step 2: Key Formula or Approach:
Moving North is an upward displacement. Making a right turn while facing North points the person Eastward. Making a subsequent right turn while facing East points the person Southward.

Step 3: Detailed Explanation:
Let's track the journey step-by-step starting from an initial origin point, let's call it $A$: 1. First Segment: The person walks 12 km North from point $A$ to arrive at point $B$. 2. Second Segment: At point $B$, turning right sets the heading East. Walking 5 km brings the person to point $C$. 3. Third Segment: At point $C$, a second right turn sets the heading South. Walking 12 km downwards brings the person to a final stopping location, point $D$. Let's evaluate the final geometric figure created by points $A \rightarrow B \rightarrow C \rightarrow D$: The vertical path segments $AB$ (12 km North) and $CD$ (12 km South) are perfectly equal in magnitude but exact opposites in direction. This symmetrical path setup creates a perfect geometric rectangle ($ABCD$). In a rectangle, opposite sides are always equal. Since side $BC = 5 \text{ km}$, its parallel opposite side representing the straight-line displacement from the start ($AD$) must also be exactly 5 km.

Step 4: Final Answer:
He is 5 km far from the starting point.