To find the length between the points (3, 2) and (7, 8), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \( (x_1, y_1) = (3, 2) \)
- \( (x_2, y_2) = (7, 8) \)
Substituting the values into the formula:
\[ d = \sqrt{(7 - 3)^2 + (8 - 2)^2} \]
Calculating inside the parentheses:
\[ d = \sqrt{(4)^2 + (6)^2} \]
Now squaring the numbers:
\[ d = \sqrt{16 + 36} \]
Adding the values:
\[ d = \sqrt{52} \]
Now simplifying the square root:
\[ d = \sqrt{4 \times 13} = 2\sqrt{13} \]
So, the length between the points (3, 2) and (7, 8) is \( 2\sqrt{13} \) or approximately \( 7.21 \) units.