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

Options

A. `5`
B. `5sqrt(2)`
C. `2sqrt(5)`
D. `10`

Explanation

To find the distance between the points \( (0, 5) \) and \( (-5, 0) \), we can use the distance formula. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:

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

### Step-by-Step Solution:

1. **Identify the coordinates of the points**:
- Let \( (x_1, y_1) = (0, 5) \)
- Let \( (x_2, y_2) = (-5, 0) \)

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 squared values**:
\[ d = \sqrt{50} \]

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

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

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