The geometric centroid (center of mass) of the polygon vertices of a triangle is the point D which is also the intersection of three triangle's medians.
The centroid theorem states that the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Since [tex] \dfrac{AD}{AE} =\dfrac{12}{12+4}=\dfrac{12}{16} =\dfrac{3}{4}\neq \dfrac{2}{3} ,[/tex] you can state that D is not centroid (options A and B are not true).
By the centroid theorem, DE should be half of AD (AD should be twice longer), then option C is false.
Since [tex] \dfrac{AD}{DE} =\dfrac{12}{4}=\dfrac{12}{16} =\dfrac{3}{1}\neq \dfrac{2}{1},[/tex] option D is true.
Answer: correct choice is D.
