# How do you find the center, circumference, and area of the circle diameter with endpoints:P(2,4) & Q(-3,16)?

Jan 21, 2017

The center of your circle would be the midpoint between (2,4) and (-3,16): $\left(\frac{2 + \left(- 3\right)}{2} , \frac{4 + 16}{2}\right)$ or $\left(- \frac{1}{2} , 10\right)$.

#### Explanation:

Now, calculate the radius from the center to either endpoint:
(Distance Formula)
$\sqrt{{\left(- \frac{1}{2} - 2\right)}^{2} + {\left(10 - 4\right)}^{2}}$ = $\sqrt{\frac{169}{4}}$ = $\frac{13}{2}$.

To calculate circumference, now use $2 \pi \cdot \frac{13}{2}$ = $13 \pi$ or about 40.84 units of length.

For area, use $\pi \cdot {\left(\frac{13}{2}\right)}^{2}$ = $\frac{169 \pi}{4}$ or $\approx 132.73$ square units.