How to find the center of mass of a right triangle?

The center of mass or centroid of a region is the point at which the region will be perfectly balanced horizontally if suspended from that point.

Answer: To find the center of mass of a right triangle, we need to find the centroid of the triangle.

Explanation:

What is the center of mass?

The center of mass is a position for an object or a group of objects defined relative to its different positions. It is the average position of the objects or system of objects, weighted according to their masses. Its unit is, therefore, similar to that of length and not mass. 

Special case:

In the case of simple rigid objects with uniform bodies, the center of mass can be supposed to be located at the centroid of that object.

In the case of a right-angled triangle, which has a uniform shape too, its center of mass can be calculated by calculating the centroid of the triangle.

For a right triangle, the centroid can be found using the following steps.

Geometric of graphical representation of the centroid of right angled-triangle.

From the right angle, firstly measure one-third of the distance along the two adjacent sides to the other given vertices.

Secondly, draw lines at right angles to the sides at the one-third points, and the intersection of the lines should be the centroid.

Formulation of the centroid:

More generally for any triangle, with vertices A, B, and C, which have coordinates (xA, yA), (xB, yB), and (xC, yC), respectively, the centroid should be located at the point:

(1/3 (x_A+ x_B+ x_C), 1/3 (y_A+ y_B+ y_C))

Thus, to find the center of mass of a right triangle, we need to find the centroid of the triangle.