A boy leaves his house. He travels 6 km towards South, then travels 8 km towards West, and further travels 9 km towards South. How far and in which direction is he from his house now?

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Accepted Answer

To determine the distance and direction:

1. **Calculate total distances traveled in each direction:**  
   - Total distance traveled South = $$6 + 9 = 15 \, 	ext{km}$$.  
   - Total distance traveled West = $$8 \, 	ext{km}$$.

2. **Use the Pythagorean theorem to calculate the straight-line distance from the starting point:**  
   - Distance = $$\sqrt{(15)^2 + (8)^2} = \sqrt{225 + 64} = \sqrt{289} = 17 \, 	ext{km}$$.

3. **Determine the direction:**  
   - Since the movement is towards South and West, the direction is **South West**.

Thus, the boy is **17 km away in the South West direction**.

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