To find the length between the two points (3, 2) and (7, 8) using the Pythagorean Theorem, we can calculate the distance \(d\) using 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 coordinates into the formula:
\[ d = \sqrt{(7 - 3)^2 + (8 - 2)^2} \] \[ = \sqrt{(4)^2 + (6)^2} \] \[ = \sqrt{16 + 36} \] \[ = \sqrt{52} \] \[ = 2\sqrt{13} \]
Now let's calculate \(2\sqrt{13}\):
First, we can find \(\sqrt{13} \approx 3.60555\)
Now we multiply by 2:
\[ 2 \cdot 3.60555 \approx 7.2111 \]
Rounding to the nearest hundredth:
\[ d \approx 7.21 \]
The length between the two points is approximately 7.21.