Question

Find the coordinates of the center C of a circle if the endpoints of itsdiameter are A(8,-4) and B(-3, 2).C(x, y) =

Answer 1

C(2.5,-1)

Explanation

Step 1

if the points A and B are the endpoints of the diameter, we can find the midpoint to find the coordiantes of the center, the midpoint of P1 and P2 is given by:

$\begin{gathered} \text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2}) \\ \text{ where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \end{gathered}$

Let

P1=A(8,-4) P2=(-3,2)

midpoint C

Step 2

replace

$\begin{gathered} \text{c}=\text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2}) \\ \text{midpoint}=(\frac{8-3}{2},\frac{-4+2}{2}) \\ \text{midpoint}=(\frac{5}{2},\frac{-2_{}}{2}) \\ \text{midpoint}=(2.5,-1) \\ \end{gathered}$

so, the answer is C(2.5,-1)