Draw the x- and y-axes on a sheet of graph paper, and plot and label the coordinates of the parallelogram. Draw lines to connect points A, B, C and D to form the parallelogram and draw the diagonal lines AC and BD.
Find the midpoints of AC and BD using the midpoint formula, which states for a line between points (x[1], y[1]), or (x sub 1, y sub 1), and (x[2], y[2]), the midpoint is ((x[1] + x[2]) / 2, (y[1] + y[2]) / 2).
Compare the given point with the calculated midpoint. For example, given parallelogram ABCD with vertices at (-2,1), (1,6), (7,6) and (4,1), calculate the midpoint of diagonal AC between points (-2,1) and (7,6): ((-2 + 7) / 2), ((1 + 6)/2) = (5/2), and diagonal BD between points (1,6) and (4,1): ((1 + 4) / 2), ((6 + 1)/2) = (7/2). Their point of intersection or the midpoint of ABCD is ( 5/2, 7/2 ) or (2.5, 3.5).