Answer:
Step-by-step explanation:
mid point of WX (say P)=((0+2a)/(2),(4b+0)/(2))=(a,2b)
mid point of XY (say Q)=((2a+0)/(2),(0-4b)/(2)=(a,-2b)
mid point of YZ (say R)=((0-2a)/(2),(-4b+0)/(2)=(-a,-2b)
mid point of WZ (say S)=((0-2a)/(2),(4b+0)/(2)=(-a,2b)
PQ=4b
QR=2a
RS=4b
WS=2a
PQ=RS
QR=WS
[tex]PR=\sqrt{(-a-a)^2+(2b+2b)^2} =\sqrt{x} =\sqrt{4a^2+16b^2} \\QS =\sqrt{(-a-a)^2+(2b+2b)^2} =\sqrt{4a^2+16b^2} \\[/tex]
PR=QS
hence opposite sides are equal and diagonals are also equal.
so it is a rectangle.
