A person goes 5 km towards the east, then turns right and goes 8 km, then turns left and goes 5 km, and finally turns left again and goes 8 km. After completing this path, what is his distance from the starting point?

Introduction / Context:
Here we have a direction sense question where the person traces a kind of rectangle, but the distances on the sides are not symmetric around the starting point. Instead of simply returning to the start, the person ends up at a point horizontally displaced from the origin. The problem asks for the straight line distance between the starting and ending points, which uses coordinate tracking and the Pythagoras theorem.

Given Data / Assumptions:

• The person walks 5 km east from the starting point.
• He then turns right and walks 8 km, which means he now travels towards the south.
• Next, he turns left and walks 5 km, which makes him travel towards the east again.
• Finally, he turns left once more and walks 8 km, which makes him travel towards the north.
• All movements are straight, and turns are ninety degree turns.

Concept / Approach:
We use coordinates with origin at the starting point. By updating x and y for each leg of the journey, we obtain the final coordinates. Because the vertical distances turn out to cancel fully, the net displacement lies entirely along the east west direction, and the distance is simply the absolute difference in x coordinates. The process demonstrates how rectangular paths can still yield non zero displacement when the side lengths are unequal around the start.

Step-by-Step Solution:
Step 1: Start at (0, 0).Step 2: Move 5 km east to reach (5, 0).Step 3: Facing east, a right turn leads to facing south. Walking 8 km south moves him to (5, -8).Step 4: From facing south, a left turn leads to facing east again. Walking 5 km east takes him to (10, -8).Step 5: From facing east, another left turn makes him face north. Walking 8 km north brings him to the final position (10, 0).Step 6: The starting point was (0, 0) and the final point is (10, 0), which means there is no vertical displacement and a net 10 km displacement towards the east.

Verification / Alternative check:
If we consider vertical movements only, the person moves 8 km south and later 8 km north, which cancel each other. For horizontal movement, he first travels 5 km east and later another 5 km east, giving a total of 10 km east without any westward movement. Therefore, his final position is 10 km east of the starting point. Since there is no north south offset, the straight line distance between the two points is exactly 10 km.

Why Other Options Are Wrong:
Option A (8 km) confuses the vertical leg with the net displacement. Option B (0 km) would be correct only if he returned to the starting point, which he does not. Option D (5 km) again reflects only one part of the total horizontal distance. Only option C correctly states that the person ends up 10 km from the starting point.

Common Pitfalls:
Candidates may mistakenly assume that whenever a rectangular path is traced, the person must return to the starting point, overlooking the possibility that the starting corner and ending corner can be different. Another pitfall is mismanaging left and right turns when the direction changes from east to south and so on. Drawing a rectangle and carefully marking the lengths and directions is often enough to see the displacement clearly.

Final Answer:
The person is finally located 10 km away from his starting point, so the correct option is “10 km”.