The line y = 3x - 8 intersects the circle x^2 + (y - 1)^2 = 10 at A and B. Find the midpoint of AB. Enter your answer in the form (x,y).
+128448 y =3x + 8
So
x^2 + [ 3x +8 -1]^2 = 10
x^2 + [3x + 7]^2 =10
x^2 + 9x^2 + 42x + 49 =10
10x^2 + 42x + 39 = 0
The sum of the two solutions to this = -42 /10 = -4.2
The x midpoint of these two solutions = [sum of two solutions / 2 ] = (-4.2 / 2 ) = -2.1
And the y coordinate of this midpoint is 3(-2.1) + 8 = 1.7
(x,y) = ( -2.1 , 1.7)
