Question

The vertices of triangle ABC are A(1,1), B(0,2), and C(3,-2). Find the coordinates of the circumcenter. ...?

Answer 1

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)

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