The angle between the diagonal of a quadrilateral formed by the lines xa+yb=1, xb+ya=1, xa+yb=2 and xa+ya=2 is
π4
π2
π3
π6
Clearly, distance between the parallel lines xa+yb=1 and xa+yb=2 is same as the distance between the parallel lines xa+yb=1 and xb+ya=2.
Therefore, quadrilateral is rhombus.