Find the distance between the points (0,0) and (36,15).

Answer

To find the distance between the points (0, 0) and (36, 15), we will use the distance formula from coordinate geometry. The distance formula is given by:

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

Where:
- \((x_1, y_1)\) are the coordinates of the first point,
- \((x_2, y_2)\) are the coordinates of the second point.

### Step 1: Identify the coordinates
Here, we have:
- Point A: \((x_1, y_1) = (0, 0)\)
- Point B: \((x_2, y_2) = (36, 15)\)

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

\[ d = \sqrt{(36 - 0)^2 + (15 - 0)^2} \]

### Step 3: Simplify the expression
Calculating the differences:
- \(x_2 - x_1 = 36 - 0 = 36\)
- \(y_2 - y_1 = 15 - 0 = 15\)

Now substituting these values into the formula:

\[ d = \sqrt{(36)^2 + (15)^2} \]

### Step 4: Calculate the squares
Now we calculate the squares:
- \(36^2 = 1296\)
- \(15^2 = 225\)

### Step 5: Add the squares
Now we add these two results:

\[ d = \sqrt{1296 + 225} \]
\[ d = \sqrt{1521} \]

### Step 6: Find the square root
Now we calculate the square root:

\[ d = 39 \]

### Conclusion
Thus, the distance between the points (0, 0) and (36, 15) is **39**.

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