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=√((x_2-x_1)^2+(y_2-y_1)^2)`

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

`d=√((8-2)^2+(-5-(-5))^2)=√(6^2+0^2)=√(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((x_1+x_2)/(2),\ (y_1+y_2)/(2)\right)`

Substitute:

`(-5+(-5))/(2)=(-10)/(2)=-5\\\\(2+8)/(2)=(10)/(2)=5`

Answer: (-5, 5).