A centroid is the centre of mass of a geometric object of uniform density. This is also the geometric centre of an object. You can find the centroid of a triangle by creating lines from each of the three vertices to the midpoint of the opposite edge. The centroid is the intersection of the lines.
a) What is the centroid of a triangle with coordinates (1,4), (4,1) and (7,7)?
b) What is the length of the line of the two centroids when the quadrilateral ABCD is cut into two triangles ABC and ADC when A(3,5), B(7,7), C(5,3) and D(2,2)?
c) Do you notice any patterns from the three centroids that you have found? Can you find a general formula for the centroid? Hint: Consider 
as the three vertices of a triangle and follow the method stated above.