centroid of the triangle

Jun 19, 2020, 16:45 IST

centroid of the triangle

Definition :-Every triangle has a single point somewhere near its "middle" that allows the triangle to balance perfectly, if the triangle is made from a rigid material. The centroid of a triangle is that balancing point, created by the intersection of the three medians.
If the triangle were cut out of some uniformly dense material, such as sturdy cardboard, sheet metal, or plywood, the centroid would be the spot where the triangle would balance on the tip of your finger.

Formula description :- The centroid is easily found coordinates: a triangle with vertices at (x1, y1), (x2, y2), (x3, y3) has centroid at

Application :-You can use the more encompassing definition of centroid: it can be used to mean the center of gravity of a 2D plane figure, not just a triangle, or the center of gravity of a 3D object as well. The center of mass is a point at which all the mass of the object may be theoretically considered to be concentrated for design purposes.

Example 1 :-Find the co-ordinates of the point of intersection of the medians of trangle ABC; given A = (-2, 3), B = (6, 7) and C = (4, 1).

Solution :-
Here,Let G (x, y) be the centroid of the triangle ABC, Then,

Therefore, the coordinates of the centroid G of the triangle ABC are Thus, the coordinates of the point of intersection of the medians of triangle areTherefore, the coordinates of the centroid G of the triangle ABC are

Example 2 :-Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.

Solution :-
Let the coordinates of the third vertex are (h, k).
Therefore, the coordinates of the centroid of the triangle

According, to the problem we know that the centroid of the given triangle is (0, 0)
Therefore,

h = –4 and K = –5
Therefore, the third vertex of the given triangle are (–4, –5).