Analytic geometry problem

Question

In the figure ABCD is a parallelogram and AE=EB if A (2,1) and C (-1,5) are given find coordinates of point P Is there any particular theorem for this problem?

Answer 1

Let DB cut AC at F. Then, F is the midpoint of DB. Further, P is the centroid of the $\triangle ADB$.

Do you know AP : PC = ?

(Further hint -- AP : PF = 2:1 because P is the centroid of $\triangle ADE$ and AF : FC = 1 : 1 because F is the middle point of the the //gm ABCD.)

If yes, you can use the section formula to find P.