Find the distance between the points `(0,-3)` and `(3,0)`

Answer

To find the distance between the points \( (0, -3) \) and \( (3, 0) \), we will 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 \( (x_1, y_1) = (0, -3) \) and \( (x_2, y_2) = (3, 0) \).

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

\[ d = \sqrt{(3 - 0)^2 + (0 - (-3))^2} \]

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

\[ d = \sqrt{(3)^2 + (0 + 3)^2} \]

This simplifies to:

\[ d = \sqrt{3^2 + 3^2} \]

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

\[ d = \sqrt{9 + 9} \]

### Step 5: Add the squares
Add the results:

\[ d = \sqrt{18} \]

### Step 6: Simplify the square root
Now, simplify \( \sqrt{18} \):

\[ d = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

### Final Answer
Thus, the distance between the points \( (0, -3) \) and \( (3, 0) \) is:

\[ \boxed{3\sqrt{2}} \text{ units} \]

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