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?
Answer & explanation
Correct answer: option 3
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
- Travels 5 km South:
$(0, 0) \to (0, -5)$ - Turns left (from South → East) and travels 5 km:
$(0, -5) \to (5, -5)$ - Turns right (from East → South) and travels 7 km:
$(5, -5) \to (5, -12)$
Step 3: Find distance from starting point
Distance formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
$d = \sqrt{(5 - 0)^2 + (-12 - 0)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ km}$