Problems on centroid of the triangle

Centroid of a Triangle

The coordinates of the centroid of a triangle are (1,3) and two of its vertices are (-7,6) and (8,5). Find the third vertex.Also find the coordinates of the centroid of the triangle when the third vertex is (2,4) .

Centroid of triangle

Points A(3,5) , B (-1,4) and C( 7,-6) are the vertices of Delta ABC. Find the coordinates of the centroid of the triangle

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

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 ?

A triangle has side lengths 18, 24 and 30. Find the area of the triangle whose vertices are the incentre, circumcentre and centroid of the triangle.

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?