The endpoints of the diameter of a circle are (-7, 3) and (5, 1). What is the center of the circle?

Solution:

We know that the center is the midpoint of the diameter of the circle.

Using the midpoint formula,

Centre, C(x\(_0\), y\(_0\)) = ((x\(_1\) + x\(_2\))/2, (y\(_1\) + y\(_2\))/2)

Given endpoints are (x\(_1\), y\(_1\)) = (-7, 3) and (x\(_2\), y\(_2\)) = (5, 1)

∴ C(x\(_0\), y\(_0\)) = ((-7 + 5)/2 , (3 + 1)/2)

C(x\(_0\), y\(_0\)) = (-1, 2)

The endpoints of the diameter of a circle are (-7, 3) and (5, 1). What is the center of the circle?

Summary:

The center of the circle, with endpoints (-7, 3) and (5, 1), is (-1, 2).