For the answer to the question above, in this case, the center is
((-10 + 4)/2, (-2 + 6)/2) = (-6/2, 4/2) = (-3,2). (To determine a midpoint you just
take the average of the x-values for the x-coordinate and the average of the
y values for the y-coordinate of the midpoint.)
b. For the radius so
r = (1/2) sqrt((4 - (-10))^2 + (6 - (-2))^2) = (1/2) sqrt(14^2 + 8^2) = (1/2)sqrt(260)
which can be simplified to (1/2)2sqrt(65) = sqrt(65).
(That is, r = (1/2) * diameter and the diameter is then calculated using the
formula for the distance between the two endpoints given.)
c. The general equation for a circle is (x-h)^2 + (y-k)^2 = r^2, center (h,k) radius r
so in this case we have (x + 3)^2 + (y - 2)^2 = 65, as r^2 = (sqrt(65))^2 = 65.
I hope my answer helped you.
