The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have two points A(-5, 2) and B(-5, 8). Substitute:
[tex]d=\sqrt{(8-2)^2+(-5-(-5))^2}=\sqrt{6^2+0^2}=\sqrt{6^2}=6[/tex]
d is a diameter of a circle because d = 2r = 2(3).
The center of a circle is in midpoint of AB.
The formula of a midpoint:
[tex]M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
Substitute:
[tex]\dfrac{-5+(-5)}{2}=\dfrac{-10}{2}=-5\\\\\dfrac{2+8}{2}=\dfrac{10}{2}=5[/tex]
Answer: (-5, 5).
