The vertices of triangle abc are a(1,1), b(0,2), and c(3,-2). find the coordinates of the circumcenter.

To find the circumcenter, solve any two bisector equations and find out the intersection points. The given are A(1,1), B(0,2), and C(3,-2).

Midpoint of AB = (1/2, 3/2)  - You can get the midpoint by getting the average of x-coordinates and y-coordinates. 

Slope of AB = -1
Slope of perpendicular bisector = 1
Equation of AB with slope 1 and the coordinates (1/2, 3/2) is
y - (3/2) = (1)(x - 1/2) 
y = x+1

Do the same for AC
Midpoint of AC = (2, -1/2)
Slope of AC = -3/2
Slope of perpendicular bisector = 2/3
Equation of AC with slope 2/3 and the coordinates (2, -1/2) is
y - (-1/2) = (2/3)(x - 2) 
y = -11/6 + 2x/3

So the perpendicular bisectors of AB and BC meet
y = x+1
y = -11/6 + 2x/3

To solve for x,
(-11/6 + 2x/3) = (x+1)
x= -17/2

Now get y by substituting 
y = (-17/2) + 1
y = -15/2

The circumcenter is (-17/2, -15/2)

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help. 

You need to include the original coordinates of the triangle to answer this. and how much does it translate (move left right up down)