SOLUTION: Points X (-1,1),Y (3,5), and Z (17,1), are the coordinates of three vertices of a parallelogram. What are the possible coordinates of W, the fourth vertex?

Algebra ->  Parallelograms -> SOLUTION: Points X (-1,1),Y (3,5), and Z (17,1), are the coordinates of three vertices of a parallelogram. What are the possible coordinates of W, the fourth vertex?      Log On


   

Question 122273: Points X (-1,1),Y (3,5), and Z (17,1), are the coordinates of three vertices of a parallelogram. What are the possible coordinates of W, the fourth vertex?
Found 2 solutions by psbhowmick, MathLover1:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
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. %28k-1%29%2F%28h-%28-1%29%29+=+%285+-+1%29%2F%283+-+17%29
i.e. %28k-1%29%2F%28h%2B1%29+=+-4%2F14+=+-2%2F7
i.e. 7%28k-1%29+=+-2%28h%2B1%29
i.e. 2h+%2B+7k+=+5%29 __________ (1)

Slope of ZW = Slope of XY
i.e. %28k-1%29%2F%28h-17%29+=+%285-1%29%2F%283-%28-1%29%29
i.e. %28k-1%29%2F%28h-17%29+=+4%2F4+=+1
i.e. %28k-1%29+=+%28h-17%29
i.e. h+-+k+=+16 _________ (2)
Solving (1) and (2)
h = 13
k = -3

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

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
one more solution is here
since YW || XZ ...=> W have y coordinates same as Y; W(x,5)
since distance between points X an Z is 1%2B17=18 units, so and distance between points Y an W is d=3%2B18=21 ...so x=21
then we have that the coordinates of W are(21,5)