What are the coordinates of the circumcenter of a triangle with vertices A(−3, 3) , B(−1, 3) , and C(−1, −1) ?
I believe its -2, -1 but i'm not sure.
The circumcenter is where the perpendicular bisectors of the triangle meet
A(−3, 3) , B(−1, 3) , and C(−1, −1)
Find the midpoint of AC = (-2, 1)
And the slope between thes two points is -2
And the slope of a perpendicular line is 1/2
So....the equation of the line that goes through (-2, 1) with a slope of 1/2 is
y = (1/2)(x + 2) + 1
y = (1/2)x + 2 (1)
And the midpoint of AB is ( -2, 3)
And the slope between these points is 0
So the equation of a perpendicular line to this one that goes through (-2,3) is x = -2 (2)
So...putting (2) into (1) we have
y = (1/2)(-2) + 2
y = -1 + 2
y = 1
So....the circumcenter is ( -2, 1)
Here's the graph :