A circle has a diameter with endpoints of (-2, 8) and (6, 4). What is the center of the circle?

Solution:

We know that

If a circle has a diameter with endpoints of (x1, y1) and (x2, y2) then the center has coordinates.

Using the midpoint formula we get the coordinates of the center as

((x\(_1\) + x\(_2\))/2, (y\(_1\) + y\(_2\))/2))

In the question, the endpoints of the circle are (-2, 8) and (6, 4)

Then the center of the circle =

((x\(_1\) + x\(_2\))/2, (y\(_1\) + y\(_2\))/2))

Substituting the values

= [(-2 + 6)/2, (8 + 4)/2]

= [4/2, 12/2]

= [2, 6]

Therefore, the center of the circle is [2, 6].

A circle has a diameter with endpoints of (-2, 8) and (6, 4). What is the center of the circle?

Summary:

A circle has a diameter with endpoints of (-2, 8) and (6, 4). The center of the circle is [2, 6].