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 will use the distance formula. The distance \( d \) between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates
Let:
- Point A: \( (x_1, y_1) = (0, 5) \)
- Point B: \( (x_2, y_2) = (-5, 0) \)

### Step 2: Substitute the coordinates into the distance formula
Now, we substitute the coordinates into the formula:

\[ d = \sqrt{((-5) - 0)^2 + (0 - 5)^2} \]

### Step 3: Simplify the expression
Calculating the differences:

\[ d = \sqrt{(-5)^2 + (-5)^2} \]

Calculating the squares:

\[ d = \sqrt{25 + 25} \]

### Step 4: Combine the results
Now, combine the results:

\[ d = \sqrt{50} \]

### Step 5: Simplify \(\sqrt{50}\)
We can simplify \(\sqrt{50}\):

\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Final Answer
Thus, the distance between the points (0, 5) and (-5, 0) is:

\[ \boxed{5\sqrt{2}} \]