To find the radius, I can use the fact that the diameter is twice the radius, and that the length of the diameter is the distance between $A$ and $B$. I can use the distance formula to find the length of the diameter: $d = \sqrt{(3 - (-1))^2 + (2 - (-2))^2} = \sqrt{16 + 16} = \sqrt{32}$. Therefore, the radius is half of that, or $r = \frac{\sqrt{32}}{2}$. Now I can plug this into the formula for the area of the circle: $A = \pi r^2 = \pi (\frac{\sqrt{32}}{2})^2 = \pi \frac{32}{4} = 8\pi$.


Points $A(-1, -2)$ and $B(3, 2)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.