Question

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

Answer 1

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

Explanation:

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.