In circle O, diameter RS has endpoints R(3a,2b-1) and S(a-6,4b+5). Find the coordinates of point O in terms of a and b. Express your answer in simplest form.

Answer 1

we know that the end points of a diameter have radially symmetric coordinates. so,

3a = -(a-6)
3a = -a + 6
4a = 6
a = 3/2

2b-1 = -(4b+5)
2b-1 = -4b-5
6b = -4
b = -2/3

R = (9/2,-7/3)
S = (-9/2,7/3)