Need to prove that the centroid of any triangle is located at the point of intersection of the medians.

Draw the related triangle.

Find the position of the intersection of the medians.

The intersection of the medians is away from a vertex on the median from that vertex.

Find the coordinates of modpoint .

is mid point between .

.

Find the distance between the coordinates of and .

Centroid is .

Find the area:

.

First find the curve equations:

The area of the triangle is .

Equation of line .

Point slope form of a lin equation is .

.

Equation of line :

.

Find the -coordinate of the centroid.

.

Find the -coordinate of the centroid.

.

Therefore, centroid is .

The centroid of any triangle is located at the point of intersection of the medians.

The centroid of any triangle is located at the point of intersection of the medians.