Question 40985
Slope of CD = {{{(2-0)/(7-1) = 1/3}}}
Slope of BC = {{{(3-0)/(0-1) = -3}}}
Slope of AB = {{{(y-3)/(x-0) = (y-3)/x}}}
Slope of AD = {{{(y-2)/(x-7)}}}


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


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


Multiplying (2) by 3 and adding with (1) we have
{{{3*3x + x = 23*3 - 9 = 69 - 9 = 60}}}
or 10x = 60
or x = 6 
Then from (2) we have {{{y = 23 - 3*6 = 5}}}


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