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

Question

asked Dec 12, 2019 158k views

1 Answer

Saylor · Answer 1 · 2019-12-16T15:46:01+0000

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).