The given vertices of the triangle are
.
Find an equation of perpendicular bisector of the side
.
The midpoint of
.
The slope of
is
.
Perpendicular bisector is normal to
and passes through the midpoint of
.
So, slope of perpendicular bisector of
is 6.
(Point-slope form)
(Substitute
,
)
(Distributive property)
(Subtract y from each side)
Find an equation of perpendicular bisector of the side
.
The midpoint of
.
The slope of
is
.
Perpendicular bisector is normal to
and passes through the midpoint of
.
So, slope of perpendicular bisector of
is
.
(Point-slope form)
(Substitute
,
)
(Product two same signs is positive)
(Multiply each side by 7)
(Distributive property)
(Subtract 4 from each side)
(Subtract 7y from each side)
Solve a system of equations to find the point of intersection of the perpendicular bisectors
So,
.
Use x value to determine the y-coordinate.
\
(Write the equation)
(Substitute
)
(Add
to each side)
(Simplify)
So, 
The coordinates of circumcenter are
.