SOLUTION: Determine the point A(x,y) so that the points A(x,y), B(0,3) C(1,0), D(7,2) will be the vertices of a parallelogram. I think it is A(5,6), but I am not sure. Thank you for your

Algebra ->  Graphs -> SOLUTION: Determine the point A(x,y) so that the points A(x,y), B(0,3) C(1,0), D(7,2) will be the vertices of a parallelogram. I think it is A(5,6), but I am not sure. Thank you for your      Log On


   

Question 40985This question is from textbook
: Determine the point A(x,y) so that the points A(x,y), B(0,3) C(1,0), D(7,2) will be the vertices of a parallelogram.
I think it is A(5,6), but I am not sure. Thank you for your help. This question is from textbook

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Slope of CD = %282-0%29%2F%287-1%29+=+1%2F3
Slope of BC = %283-0%29%2F%280-1%29+=+-3
Slope of AB = %28y-3%29%2F%28x-0%29+=+%28y-3%29%2Fx
Slope of AD = %28y-2%29%2F%28x-7%29

As ABCD is a parallelogram so AB and CD are parallel and hence their slopes equal.
So %28y-3%29%2Fx+=+1%2F3
or 3(y-3) = x
or x - 3y = -9 __________(1)

Also AD and BC are parallel and hence their slopes equal.
So %28y-2%29%2F%28x-7%29+=+-3
or (y-2) = -3(x-7)
or y + 3x = 23 ____________(2)

Multiplying (2) by 3 and adding with (1) we have
3%2A3x+%2B+x+=+23%2A3+-+9+=+69+-+9+=+60
or 10x = 60
or x = 6
Then from (2) we have y+=+23+-+3%2A6+=+5

Hence the coordinates of A are (6,5).