ANSWER
The circumcenter of ∆ABC has coordinates
[tex](-2,1)[/tex]
EXPLANATION
The circumcenter is the point of intersection of the perpendicular bisectors of any two sides of triangle ABC.
Considering side AB with coordinates (-3,3) and (-1,3) respectively, we can see that this is a horizontal line. The perpendicular bisector of this line is a vertical line that has equation x equals the x-coordinate of the midpoint of AB.
Midpoint of AB has coordinates
[tex]( \frac{ - 3 + - 1}{2} , \frac{3 + 3}{2} )[/tex]
This gives
[tex]( \frac{ - 4}{2} , \frac{6}{2} )[/tex]
[tex]( - 2, 3)[/tex]
The equation of the perpendicular bisector is
[tex]x = - 2[/tex]
Similarly, the coordinates of B(-1,3) and C(-1,-1) tells us that, line BC is a horizontal line since the x-values are constant. Therefore the perpendicular bisector is a horizontal line that has equation , y equals the y-value of the midpoint of BC.
The midpoint of BC has coordinates,
[tex]( \frac{ - 1 + - 1}{2} , \frac{3 + - 1}{2} )[/tex]
This implies that,
[tex]( \frac{ - 2}{2} , \frac{2}{2} )[/tex]
This gives,
[tex]( - 1 , 1)[/tex]
The equation of the perpendicular bisector is
[tex]y = 1[/tex]
These two bisectors will meet at,
[tex](-2,1)[/tex]
Therefore the circumcenter is
[tex](-2,1).[/tex]
