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

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) (Show Source): You can put this solution on YOUR website!
Slope of CD =
Slope of BC =
Slope of AB =
Slope of AD =

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

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

Multiplying (2) by 3 and adding with (1) we have

or 10x = 60
or x = 6
Then from (2) we have

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