Find the distance of a point P(m,n) from the orgin.

Answer

To find the distance of a point P(m, n) from the origin (0, 0), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- The coordinates of point P are given as (m, n).
- The coordinates of the origin are (0, 0).

2. **Recall the Distance Formula**:
- The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

3. **Assign the Coordinates**:
- Here, we can assign:
- \( x_1 = m \), \( y_1 = n \) (coordinates of point P)
- \( x_2 = 0 \), \( y_2 = 0 \) (coordinates of the origin)

4. **Substitute the Values into the Formula**:
- Substitute the coordinates into the distance formula:
\[ d = \sqrt{(0 - m)^2 + (0 - n)^2} \]

5. **Simplify the Expression**:
- This simplifies to:
\[ d = \sqrt{(-m)^2 + (-n)^2} \]
- Since squaring a negative number gives a positive result:
\[ d = \sqrt{m^2 + n^2} \]

6. **Final Result**:
- Therefore, the distance of point P(m, n) from the origin (0, 0) is:
\[ d = \sqrt{m^2 + n^2} \]