The diagonals of the Varignon parallelogram are the

The point where the bimedians intersect is the barycenter, centroid, or center of gravity, the balance point of equal weights placed at the vertices of the quadrilateral. If the coordinates of the vertices are known, the coordinates of the intersection of the bimedians would have an x-coordinate that was the average of the x-coordinates of the vertices, and similarly for the y-coordinate. Additional information about the centroid of the general quadrilateral is found at the link to centroid.