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.

Acceptfully Nov 21, 2017

#1**+2 **

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 :

CPhill Nov 21, 2017