Question 122273
Let the coordinates of W be (h,k).
The opposite sides of a parallelogram are parallel and hence their slopes must be equal.
Slope of WX = Slope of YZ
i.e. {{{(k-1)/(h-(-1)) = (5 - 1)/(3 - 17)}}}
i.e. {{{(k-1)/(h+1) = -4/14 = -2/7}}}
i.e. {{{7(k-1) = -2(h+1)}}}
i.e. {{{2h + 7k = 5)}}} __________ (1)


Slope of ZW = Slope of XY
i.e. {{{(k-1)/(h-17) = (5-1)/(3-(-1))}}}
i.e. {{{(k-1)/(h-17) = 4/4 = 1}}}
i.e. {{{(k-1) = (h-17)}}}
i.e. {{{h - k = 16}}} _________ (2)

Solving (1) and (2)
h = 13
k = -3


Hence, the coordinates of W are (13, -3).