The endpoints of the diameter of a circle are at (-12, 14) and (6, 4). What is the location of the center of the circle?

Answer 1

Take the average of the two x coordinates and the average of the two y coordinates.

x = (x₁ + x₂)/2 = (-12 + 6)/2 = -3

y = (y₁ + y₂)/2 = (14 + 4)/2 = 9

The center is at (-3,9).

Answer 2

Hello Grace,

There are several ways of solving this problem, but perhaps the simplest way is use the idea that the radius of a circle is the midpoint of the line segment between these two endpoints, because they are the endpoints of the diameter of the circle.

To compute the midpoint of this line segment, you compute the average or mean of the two coordinates;

in this particular example, the x coordinate is given by

(-12+6)/2 = 3

and the y coordinate is given by

(14+4)/2 = 9.

Thus, the center of the circle is (3,9). Try doing the same problem, with the new endpoints being (-5,0) and (5,0), and try drawing that one out to understand why this simple trick works for this problem.

Best,

Juan B