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

Options

A. 5
B. `5sqrt2`
C. `2sqrt5`
D. 10

Answer

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

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

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

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

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

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

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

### Step 4: Calculate the squares
Now calculate the squares:

\[ d = \sqrt{25 + 25} \]
\[ d = \sqrt{50} \]

### Step 5: Simplify the square root
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 (-5, 0) and (0, 5) is:

\[ \text{Distance} = 5\sqrt{2} \text{ units} \]

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