### Instruction: Points $A(3,5)$ and $B(7,10)$ 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 $\pi$.### Response: Let's start by finding the length of the diameter.
We can use the distance formula to find the distance between the two points.
The distance formula is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
So the length of the diameter is $\sqrt{(7-3)^2+(10-5)^2}$.
Which is $\sqrt{4^2+5^2}$.
So the length of the diameter is $\sqrt{16+25}$.
So the length of the diameter is $\sqrt{41}$.
We know that the area of the circle is $\pi r^2$.
We also know that $r=\frac{d}{2}$.
So the area of the circle is $\pi \left(\frac{d}{2}\right)^2$.
So the area of the circle is $\pi \left(\frac{\sqrt{41}}{2}\right)^2$.
So the area of the circle is $\pi \frac{41}{4}$.