Let P be the; point of intersection of diagonals of a parallelogram, which is the midpoint of AB and OC.
Midpoint of AC = \((\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})\)
Midpoint of BD = \((\frac{x_2+x_4}{2},\frac{y_2+y_4}{2})\)
Midpoint of AC = Midpoint of BD
\((\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})\) = \((\frac{x_2+x_4}{2},\frac{y_2+y_4}{2})\)
Comparing x coordinates
\(\frac{x_1+x_3}{2}=\frac{x_2+x_4}{2}\)
x1 + x3 = x2 + x4
From eqn
Comparing y coordinates
\(\frac{y_1+y_3}{2}=\frac{y_2+y_4}{2}\)
y1 + y3 = y2 + y4
