Question

the center of circle P is located at (5,-2)
ST is a diameter of circle P.
point T is located (-3,3).
what are the coordinates of point S??

Answer 1

Since ST is a diameter, the center of the circle will be at the midpoint of S and T.

Answer 2

Let (a,b) be the coordinates of point S.
T is (-3,3)
The midpoint of ST is: ( (a-3)/2, (b+3)/2 )
which should be the center of the circle (5, -2)
Equate the x-coordinates and solve for a: (a-3)/2 = 5; a-3 = 10; a = 13
Equate the y-coordinates and solve for b: (b+3)/2 = -2; b+3 = -4; b = -7

Coordinates of S is (13, -7).