Question

What are the coordinates of the circumcenter of a triangle with vertices A(−3,−4), B(1,−4), and C(−3,0)?

Answer 1

the coordinate of the circumecenter of a triangle is A

Answer 2

The circumcenter is equal distance from all 3 verices.
Using distance formula, equate distance to A with distance to C:
$(x+3)^2 +(y+4)^2 = (x+3)^2 + y^2$
The x terms cancel, Expand and solve for y:
$y^2 +8y+16 = y^2$
$y = -2$
Now do same thing for point A and B:
$(x+3)^2 + (y+4)^2 = (x-1)^2 + (y+4)^2$
y terms cancel
$x^2 +6x+9 = x^2-2x+1$
$x = -1$

Circumcenter is the point (-1,-2)