The vertices of the parallelogram are  and .

Need to prove that the centroid of the parallelogram is the point of intersection of the diagonals.

Draw the related parallelogram.

Find the position of the intersection of the medians.

Equation of line .

Point slope form of a line equation is .

Equation of line .

.

The intersection point of  and .

.

Substitute  in .

.

The point of intersection is .

Find the area of parallelogram.

The area of the parallelogram is .

Substitute  and .

.

.

First find the curve equations:

Equation of line .

Point slope form of a line equation is .

.

Consider .

Equation of line :

.

Consider .

Find the -coordinate of the centroid.

.

.

Find the -coordinate of the centroid.

.

.

Therefore, centroid is .

The centroid of parallelogram is located at the point of intersection of the diagonals.

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