A person walks 10 meters facing North, turns left and walks 15 meters, turns left again and walks 10 meters, and finally turns right and walks 20 meters. How far and in which direction is he from the starting point?

Question

Accepted Answer

Let's track the movements step-by-step using a Cartesian coordinate system (starting point at origin $(0,0)$):

1. **Starts at $(0,0)$ and walks 10m North:** 
   * Position: $(0, 10)$ (Facing North)
2. **Turns left (West) and walks 15m:** 
   * Position: $(-15, 10)$ (Facing West)
3. **Turns left (South) and walks 10m:** 
   * Position: $(-15, 10 - 10) = (-15, 0)$ (Facing South)
4. **Turns right (West) and walks 20m:** 
   * Position: $(-15 - 20, 0) = (-35, 0)$ (Facing West)

### Final Calculation:
* Final coordinates: $(-35, 0)$.
* **Distance from starting point $(0,0)$:** $\sqrt{(-35-0)^2 + (0-0)^2} = 35$ meters.
* **Direction from starting point:** Since the x-coordinate is negative and y is 0, he is due **West** of the starting point.

**Answer:** He is **35 meters West** from the starting point.

A person walks 10 meters facing North, turns left and walks 15 meters, turns left again and walks 10 meters, and finally turns right and walks 20 meters. How far and in which direction is he from the starting point? - DDCET Q&A

A person walks 10 meters facing North, turns left and walks 15 meters, turns left again and walks 10 meters, and finally turns right and walks 20 meters. How far and in which direction is he from the starting point?

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