representing geometric figures on the coordinate system. can you help?

Question

help with this geomitry problem
(sorry if this is not in a questionable form yet i dont know how to)


three vertices of a parralelogram are shown on the coordinate grid. what ae the coordinates of point Z that from parrallelogram wxyz?

w=(-5,0)
x=(-2,-4)
y= (3,-5)
Z= (?,?)

Answer 1

Yes. Z is the point (0, -1).

I got this by arguing I had to:

(i) SUBTRACT 3 (the difference between the x-values for points X and W, in the sense [that of X - that of W]) from the x-value of Y), and

(ii) ADD 4 (the difference between the y-values for points W and X, in the sense [that of W - that of X]) to the y-value of Y).

(Why these particular operations are required can be made clear by the crudest of sketches. Doing these two operations simultaneously ensures that the new side YZ has both the correct LENGTH and the correct SLOPE to be the side parallel to XW.)

The operations just described are those needed to ensure that side YZ is parallel to side XZ (in that order).

That the point (0, 1) is indeed correct can now be checked by similarly examining whether it makes the side WZ parallel to the side XY (in that order). It does!

Live long and prosper.

Answer 2

Hint: the slope of the lines wx and yz should be the same, because they are parallel. Also the slope of the lines wz and xy should be the same.