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

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

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.

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To find the centroid of a triangle, you need to find the point of intersection of its medians. Each median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Given the equations of the perpendicular bisectors, you first need to find the intersection points of these lines. Then, you find the midpoints of the sides of the triangle. Finally, you find the centroid, which is the point of intersection of the medians.

To find the intersection points of the perpendicular bisectors, you solve pairs of equations. Then, you find the midpoints of the sides by averaging the coordinates of the endpoints. Finally, you find the centroid by averaging the coordinates of the vertices of the triangle.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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