Question

if MN is the diameter of the circle, with M (-3,-4) and N (-7,-14) find the center of the circle

Answer 1

Well you know that halfway of the diameter is the center...so we just need to find the mid point...

For the x-coordinate
\[\large \frac{ x_1 + x_2 }{ 2 }\]
\[\large \frac{ -3 - 7 }{ 2 }\]
\[\large \frac{ -10 }{ 2 }\]
\[\large -5 \]

and for the y-coordinate

\[\large \frac{ y_1 + y_2 }{ 2 }\]
\[\large \frac{ -14 - 4 }{ 2 }\]
\[\large \frac{ -18 }{ 2 }\]
\[\large -9\]

so your center is..\(\large (-5 , -9) \)