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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
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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

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