Coordinate geometry help

Question

A Circle Has A Center Of (2,-2). The Diameter Has One Endpoint Of (4,2). What Are The Coordinates Of The Other Endpoint?

Answer 1

Let (x,y) be the unknown endpoint of the diameter.

 

Since the center of the circle is the midpoint of any diameter, we have:

 

(x+4)/2 = 2 and (y+2)/2 = -2

 

So, x = 0 and y = -6

 

(x,y) = (0,-6)