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

Options

A. 3kms
B. 4kms
C. 5 kms
D. 7 kms

Explanation

To solve the problem step by step, we will analyze the movements of the man and calculate his final distance from the starting point.

### Step-by-Step Solution

1. **Starting Point**: Let's denote the starting point as O.

2. **First Movement**: The man walks 1 km towards the East.
- New position: A (1 km East of O)

3. **Second Movement**: He then turns South and walks 5 km.
- New position: B (5 km South of A)
- Coordinates: A (1, 0) → B (1, -5)

4. **Third Movement**: He turns to the East again and walks 2 km.
- New position: C (2 km East of B)
- Coordinates: B (1, -5) → C (3, -5)

5. **Fourth Movement**: Finally, he turns North and walks 9 km.
- New position: D (9 km North of C)
- Coordinates: C (3, -5) → D (3, 4)

6. **Finding the Distance**: Now, we need to find the distance from the starting point O (0, 0) to the final position D (3, 4).
- We will use the distance formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (3, 4) \).
- Plugging in the values:
\[ \text{Distance} = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km} \]

### Final Answer
The man is **5 km** away from his starting point.

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