Question

HELP ASAP 25 POINTS!!!

What is the center of the circle that has a diameter whose endpoints are (-3, -5) and (-11, -7)?

(-8, -1)
(-7, -6)
(-4, -6)

Answer 1

The diameter of a circle by definition goes from one "side" of the circle to the other "side" and goes through the center. If we are given the coordinates of the endpoints of the diameter, we need to find the midpoint of that segment to find the center of the circle. The midpoint formula is as follows
`M=( ( x_(1)+ x_(2) )/(2), ( y_(1)+ y_(2) )/(2))`. Filling in accordingly, we have
`M=( (-3+(-11))/(2), (-5+(-7))/(2))`. Doing the math on that gives us a midpoint of (-7, -6), which is also the center of the circle.