Show that the line joining the centroid of a triangle to its vertices divide it into three triangles of equal area.

Show that a median of a triangle divides it into two triangles of equal area.

Show that a median of a triangle divides it into two triangles of equal areas.

A diagonal of a parallelogram divides it into two triangles of equal area.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

If A(4,-6),B(3,-2) and C(5,2) are the vertices of $ABC, then verify the fact that a median of a triangle ABC divides it into two triangles of equal areas.

Find the centroid of the triangle ABC whose vertices are A (9, 2), B (1, 10) and C (-7, -6) . Find the coordinates of the middle points of its sides and hence find the centroid of the triangle formed by joining these middle points. Do the two triangles have same centroid?

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

If the centroid of the triangle having its vertices (1,a),(2,b) and (c^2,-3) lies on x axis then a+b is equal to