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This is sometimes referred to as center of mass, as well. If you could take the vector sum of all the torques produced by all of the 'point-masses' to this particular point they will net to zero. For simplicity, consider a weightless see-saw.

On the right side of the see-saw is a person weighing 100 pounds, who is 6 feet away from the pivot point. This produces (100 pounds force) x (6 feet ) = 600 foot-pounds force of torque, in the clockwise direction. On the other side of the see saw is a 200 pound person at 3 feet away from the pivot. This will produce (200 pounds force) x (3 feet ) = 600 foot-pounds force of torque, in the counter-clockwise direction. So the see-saw is balanced.

Now for each 'point-mass' (this is an infintessimaly small area with an associated small mass), a certain distance away from the centroid, there would be an equal mass the same distance away on the other side, but a vertex is farther away than the opposite side, so there will be two points, each at an angle from the centroid to a point which are a shorter distance, but add to balance the farther points. This is kind-of hard to explain without pictures.

Q: Why is the centroid the balancing point of a triangle?

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It is the triangle's point of equilibrium or its point of balance.

Medians

centroid

The centroid - which is where the medians meet.

The centroid, which is the point where the medians meet.

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the centroid is the balance point of the triangle

It is the triangle's point of equilibrium or its point of balance.

The centroid of a triangle is the point of intersection of its three medians. Each median of a triangle connects a vertex to the midpoint of the opposite side. The centroid divides each median into two segments with a ratio of 2:1, closer to the vertex.

Medians

Centroid

Centroid .

centroid

Centroid

The point where the three medians of a triangle intersect is called the centroid of the triangle.

The Centroid

centroid is the name