Rana drove 8 miles due west, then 6 miles due north, then 3 miles due east and then 6 more miles due north. The distance between his initial and final position is.
राणा ने वाहन को 8 मील पश्चिम की ओर चलाया, फिर 6 मील उत्तर की ओर, फिर 3 मील पूर्व की ओर और फिर 6 मील उत्तर की ओर। उसके आरंभिक स्थान और अंतिम स्थान में दूरी है

Options

A. 13 मील
B. 17 मील
C. 19 मील
D. 21 मील

Explanation

To find the distance between Rana's initial and final position, we can break down his journey step by step and use the Pythagorean theorem.

### Step-by-Step Solution:

1. **Starting Point**: Let's denote Rana's starting point as point O (0,0).

2. **First Move (8 miles due west)**:
- Moving west means moving in the negative x-direction.
- New position after this move:
\[ (-8, 0) \]

3. **Second Move (6 miles due north)**:
- Moving north means moving in the positive y-direction.
- New position after this move:
\[ (-8, 6) \]

4. **Third Move (3 miles due east)**:
- Moving east means moving in the positive x-direction.
- New position after this move:
\[ (-8 + 3, 6) = (-5, 6) \]

5. **Fourth Move (6 miles due north)**:
- Again moving north.
- New position after this move:
\[ (-5, 6 + 6) = (-5, 12) \]

6. **Final Position**: Rana's final position is at point F (-5, 12).

7. **Calculating the Distance**:
- We need to calculate the distance between the initial point O (0, 0) and the final point F (-5, 12).
- Using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Substituting the coordinates:
\[ d = \sqrt{((-5) - 0)^2 + (12 - 0)^2} \]
\[ = \sqrt{(-5)^2 + 12^2} \]
\[ = \sqrt{25 + 144} \]
\[ = \sqrt{169} \]
\[ = 13 \]

Thus, the distance between Rana's initial and final position is **13 miles**.