Find the distance between the points (3,6) and (0,2)

Answer

To find the distance between the points (3, 6) and (0, 2), we will use the distance formula. The distance formula is given by:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

### Step-by-Step Solution:

1. **Identify the coordinates**:
- Let \((x_1, y_1) = (3, 6)\)
- Let \((x_2, y_2) = (0, 2)\)

2. **Substitute the values into the distance formula**:
\[ d = \sqrt{(3 - 0)^2 + (6 - 2)^2} \]

3. **Calculate the differences**:
- \(x_1 - x_2 = 3 - 0 = 3\)
- \(y_1 - y_2 = 6 - 2 = 4\)

4. **Square the differences**:
\[ d = \sqrt{(3)^2 + (4)^2} \]
\[ d = \sqrt{9 + 16} \]

5. **Add the squares**:
\[ d = \sqrt{25} \]

6. **Take the square root**:
\[ d = 5 \]

### Final Answer:
The distance between the points (3, 6) and (0, 2) is **5 units**.