A boy travels 5 km towards the South and then turns left and travels 5 km. After that, he turns to his right and walks 7 km. How far is he from the starting point finally?

13 km

The correct answer is Option (3) → 13 km

Step 1: Set up coordinate system

• Start at origin: (0, 0)
• Directions: North (+y), East (+x), South (−y), West (−x)

Step 2: Track the boy’s movement

1. Travels 5 km South:
   $(0, 0) \to (0, -5)$
2. Turns left (from South → East) and travels 5 km:
   $(0, -5) \to (5, -5)$
3. Turns right (from East → South) and travels 7 km:
   $(5, -5) \to (5, -12)$

Step 3: Find distance from starting point

Distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$d = \sqrt{(5 - 0)^2 + (-12 - 0)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ km}$