Question

The points -5,2 and -5,8 lie on a circle with a radius of 3. Find the center of the circle.

Answer 1

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have two points A(-5, 2) and B(-5, 8). Substitute:

$d=\sqrt{(8-2)^2+(-5-(-5))^2}=\sqrt{6^2+0^2}=\sqrt{6^2}=6$

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:

$M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

Substitute:

$\dfrac{-5+(-5)}{2}=\dfrac{-10}{2}=-5\\\\\dfrac{2+8}{2}=\dfrac{10}{2}=5$

Answer: (-5, 5).