A person walks 1 km towards East and then he turns to South and walks 5 km. Again he turns to East and walks 2 km, after this he turns to North and walks 9 km. Now, how far is he from his starting point ?

Question

Accepted Answer

To determine how far the person is from the starting point, we need to analyze the path taken step by step and calculate the resultant distance from the starting point.

1. **Initial Position and Movement:**
   - The person starts at the origin point (0,0).
   - Walks 1 km towards East: New position is (1,0).

2. **Second Movement:**
   - Turns South and walks 5 km: New position is (1,-5).

3. **Third Movement:**
   - Turns East and walks 2 km: New position is (3,-5).

4. **Fourth Movement:**
   - Turns North and walks 9 km: New position is (3,4).

Now, we need to calculate the distance from the starting point (0,0) to the final position (3,4).

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula:
$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Substituting the coordinates of the starting point (0,0) and the final position (3,4):
$$ \text{Distance} = \sqrt{(3 - 0)^2 + (4 - 0)^2} $$
$$ \text{Distance} = \sqrt{3^2 + 4^2} $$
$$ \text{Distance} = \sqrt{9 + 16} $$
$$ \text{Distance} = \sqrt{25} $$
$$ \text{Distance} = 5 \text{ km} $$

Thus, the person is 5 km away from the starting point, which confirms that Option 2 is correct.

**Explanation for Incorrect Options:**

- **Option 1 (4 km):** This option is incorrect because the calculated distance using the Pythagorean theorem is 5 km, not 4 km. The coordinates and movements do not support a distance of 4 km.

- **Option 3 (7 km):** This option is incorrect because the calculated distance is 5 km. A distance of 7 km would imply a different set of movements or calculations, which is not the case here.

- **Option 4 (9 km):** This option is incorrect because the calculated distance is 5 km. A distance of 9 km would suggest a much longer path or different coordinates, which do not match the given movements.

Therefore, the correct answer is Option 2, as the person is indeed 5 km away from the starting point.