Perpendicular bisectors of sides of a triangle are $y=-x+4$ , $y=-3x+6$ and $y=-1/2x+7/2$ . What is its centroid?

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Answer 1 · 2017-07-22T15:13:17

$(1,3)$ is the circumcenter. The information is not sufficient to find centroid, which is the point of intersections of all medians.

As all perpendicular bisectors of a triangle intersect each other at circumcenter, let us find it.

Equations $y=-x+4$ and $y=-3x+6$ gives $x=1$ and $y=3$

and as $(1,3)$ satisfies $y=-1/2x+7/2$

$(1,3)$ is the circumcenter.

graph{(y+x-4)(y+3x-6)(2y+x-7)=0 [-9.46, 10.54, -2.08, 7.92]}

The information is not sufficient to find centroid, which is the point of intersections of all medians.

Perpendicular bisectors of sides of a triangle are y=-x+4y=-x+4, y=-3x+6y=-3x+6 and y=-1/2x+7/2y=-1/2x+7/2. What is its centroid?