The equations of the sides of a parallelogram are x=2,x=3 and y=1,y=5 .Equations to the pair of diagonals are
4x+y=7,4x−y=13
x+4y=13,x−4y=7
x+4y=7,x−4y=13
4x+y=13,4x−y=7
The vertices of the parallelogram are
A(2,1),B(2,5),C(3,5) and D(3,1)
Equation of the diagonal AC is
y−1=5−13−2(x−2)⇒4x−y=7
Equation of the diagonal BD is
y−5=1−53−2(x−2)⇒4x+y=13