Two sides of a parallelogram are along the lines x+y=3 and x−y+3=0 . If its  diagonals intersect at (2,4) then one of its vertex is

solving the given equations A(0,3) and  P2,4 is the midpoint using midpoint formula we get C(4,5)given lines are perpendicular hence the figure formed is a rectanglelet the equation of BC be x-y+k=0 sub C we get k=1let the equation of CD be x+y+c=0 sub C we get c=-9solving BC and AB we get B(1,2)solving CD and AD we get D(3,6) D3,6