Answer:
The diagonals are bisectors of each other and meet at (1, -5/2) but are not congruent, so WXYZ is a parallelogram and not a rectangle
Step-by-step explanation:
for parallelograms.
the diagonals intersect at the midpoints
W X
Z Y
Diagonals are WY and XZ
WY : (-4, -3) to (6, -2)
midpoint is [(-4 + 6)/2 , (-3 - 2)/2 ] = ( 1, -5/2 )
XZ : (0, -1) to (2, -4)
midpoint is [ (0 + 2)/2 , (-1 + -4)/2 ] = (1, -5/2)
The diagonals are bisectors of eachother.
Next show that these diagonals are not congruent.
length of WY = root ( (-4 - 6)^2 + (-3 - (-2))^2 )
WY = root ( 100 + 1)
WY = root(101)
length of XZ = root ( (0 - 2)^2 + ( -1 - -4)^2 )
XZ = root (4 + 9) = root (13)
we see that WY is not equal to XZ
...
so .. quadrilateral WXYZ is a parallelogram but not a rectangle.
