Prove that the centroid of any triangle is the same as the centroid of the triangle formed by joining the middle points of its sides

Prove that the area of any triangle is equal to four times the area of the triangle formed by joining the mid points of its sides.

prove that the area of a triangle is four times the area of the triangle formed by joining the mid-points of its sides.

prove that the area of a triangle is four times the area of the triangle formed by joining the mid-points of its sides.

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?

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?

If Delta_(1) is the area of the triangle formed by the centroid and two vertices of a triangle Delta_(2) is the area of the triangle formed by the mid- point of the sides of the same triangle, then Delta_(1):Delta_(2) =

If Delta_(1) is the area of the triangle formed by the centroid and two vertices of a triangle Delta_(2) is the area of the triangle formed by the mid- point of the sides of the same triangle, then Delta_(1):Delta_(2) =

The centroid of the triangle formed by the points (1,2),(2,4)and (-3,6) is -

The semiperimeter of a triangle is S and its centroid is G. What is the distance between G and centroid of the triangle formed by mid points of the sides of the given triangle ?