To find the circumcenter, solve any two bisector equations and find out the intersection points. The given are <span>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 </span>Equation of AB with slope 1 and the coordinates (1/2, 3/2) is <span>y - (3/2) = (1)(x - 1/2) </span><span>y = x+1
Do the same for AC </span>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 <span>the perpendicular bisectors of AB and BC meet </span>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)
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