# If the endpoints of the diameter of a circle are (7, 8) and (-2, 12), what are the coordinates of the center of the circle?

Feb 11, 2016

centre = $\left(\frac{5}{2} , 10\right)$

#### Explanation:

The centre of the circle is at the mid-point of the diameter. Hence to find coords of centre , find the mid-point of the end points.

hence :$\left[\frac{1}{2} \left({x}_{1} + {x}_{2}\right) , \frac{1}{2} \left({y}_{1} + {y}_{2}\right)\right]$

let $\left({x}_{1} , {y}_{1}\right) = \left(7 , 8\right) \textcolor{b l a c k}{\text{ and }} \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 12\right)$

substitute these values into the formula:

$\Rightarrow \left[\frac{1}{2} \left(7 - 2\right) , \frac{1}{2} \left(8 + 12\right)\right] = \left(\frac{5}{2} , 10\right)$