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Answer 1 · 2017-04-06T03:33:37

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The coordinates of mid point of the diagonal AC #((x+4)/2,(y+7)/2)#

The coordinates of mid point of the diagonal BD #((5+2)/2,(8-4)/2)=(7/2,2)#

Since ABCD is a parallelogram its diagonals will bisect each other.

So

#(x+4)/2=7/2=>x=3#

and

#(y+7)/2=2=>y=-3#

Hence coordinates of A #=(3,-3)#

Equation of the straight line passing through #B(5,8),D(2,-4)#

#(y-8)=((8+4))/((5-2))(x-5)#

#=>(y-8)=3(x-5)#

#=>(y-8)=3x-15#

#=>3x-y=7#