Apply the Pythagorean Theorem to find the length between (2,7) and (−2, 0). Round your answer to the nearest hundredth, if necessary.

To find the length between the points \((2, 7)\) and \((-2, 0)\) using the Pythagorean theorem, we first need to calculate the differences in the x-coordinates and the y-coordinates.

1. Calculate the difference in the x-coordinates:
\[
\Delta x = x_2 - x_1 = -2 - 2 = -4
\]

2. Calculate the difference in the y-coordinates:
\[
\Delta y = y_2 - y_1 = 0 - 7 = -7
\]

Now, we can use these differences to calculate the distance \(d\) between the two points using the distance formula, which is derived from the Pythagorean theorem:

\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]

Substituting \(\Delta x\) and \(\Delta y\) into the formula:

\[
d = \sqrt{(-4)^2 + (-7)^2}
\]

Calculating the squares:

\[
d = \sqrt{16 + 49}
\]

Adding these values together:

\[
d = \sqrt{65}
\]

Now, let's calculate \(\sqrt{65}\):

\[
\sqrt{65} \approx 8.0623
\]

Rounding to the nearest hundredth, the distance \(d\) is:

\[
\boxed{8.06}
\]