The distance between the point (0, 5) and (-5, 0) is

Options

A. `2sqrt(5)`
B. `5sqrt(2)`
C. 5
D. 0

Answer

To find the distance between the points (0, 5) and (-5, 0), we will use the distance formula in coordinate geometry. 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 coordinates**:
- Let point A be (0, 5) which gives us \(x_1 = 0\) and \(y_1 = 5\).
- Let point B be (-5, 0) which gives us \(x_2 = -5\) and \(y_2 = 0\).

2. **Substitute the coordinates into the distance formula**:
\[ d = \sqrt{((-5) - 0)^2 + (0 - 5)^2} \]

3. **Calculate \(x_2 - x_1\)**:
\[ x_2 - x_1 = -5 - 0 = -5 \]
So, \((-5)^2 = 25\).

4. **Calculate \(y_2 - y_1\)**:
\[ y_2 - y_1 = 0 - 5 = -5 \]
So, \((-5)^2 = 25\).

5. **Combine the results**:
\[ d = \sqrt{25 + 25} = \sqrt{50} \]

6. **Simplify \(\sqrt{50}\)**:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

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