Find the distance between (0, 5) and (-5, 0) is _______

Answer

To find the distance between the points (0, 5) and (-5, 0), we will use the distance formula. The distance formula is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step-by-Step Solution:

1. **Identify the Points:**
- Let the first point \( (x_1, y_1) = (0, 5) \)
- Let the second point \( (x_2, y_2) = (-5, 0) \)

2. **Substitute the Coordinates into the Distance Formula:**
\[ d = \sqrt{((-5) - 0)^2 + (0 - 5)^2} \]

3. **Calculate the Differences:**
- \( x_2 - x_1 = -5 - 0 = -5 \)
- \( y_2 - y_1 = 0 - 5 = -5 \)

4. **Square the Differences:**
\[ d = \sqrt{(-5)^2 + (-5)^2} \]
\[ d = \sqrt{25 + 25} \]

5. **Add the Squares:**
\[ d = \sqrt{50} \]

6. **Simplify the Square Root:**
\[ d = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Final Answer:
The distance between the points (0, 5) and (-5, 0) is \( 5\sqrt{2} \).