Varignon Parallelogram

    When the midpoints of any quadrilateral are joined in order, they form a parallelogram.  This theorem is due to a French mathematician named Pierre Varignon (1654-1722).  The resulting parallelogram is named in his honor.
   The diagonals of the Varignon parallelogram are the bimedians of the original quadrilateral, the lines which connect the midpoints of the opposite sides.
 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.