Question

what are the coordinates of that center of a circle if the endpoints of its diameter are a(8,-4) and b(-3,2)?

Answer 1

You need to add 8 and -3 together to get 5 and divide 5 by 2 to get 2.5
That is the x coordinate
You then need to add 2 and -4 together to get -2 and divide by 2 to get -1
This is the y coordinate
(2.5,-1)

Answer 2

The coordinates of that center of a circle with endpoints of its diameter at a(8,-4) and b(-3,2) is (2.5, -1)

The standard equation of a circle is:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the diameter endpoints at a(8,-4) and b(-3,2), let (x, y) be the center of the circle, hence:

$x=\frac{8-3}{2} =2.5\\\\y=\frac{-4+2}{2}=-1$

Hence the center of the circle is at (2.5, -1)

The coordinates of that center of a circle with endpoints of its diameter at a(8,-4) and b(-3,2) is (2.5, -1)