Points a(-2, 4), b(1, 3), c(4, -1) and d form a parallelogram. what are the coordinates of d? (5, 5) (0, 0) (1, -2) (1, 0) (3, 4)

If its a ABCD parallelogram ,
then, let , D(x,y)
so DA= 
BC=
    =
    =
According to question , 
=    
[Because, DA||BC]
or, (x-2)²+(y+4)²=29.....(1)
 Again,
CD=  
and AB=
           =
           =
According to question,
(x+4)²+(y-1)²=50.......(2)
[Because,CD||AB]
From (1),
x²-4x+4+y²+8y+16=29
x²+y²-4x+8y=29.....(3)
from (2),
x²+8x+16+y²-2y+1=50
x²+y²+8x-2y=33.....(4)
From(3)-(4),
-12x+10y=-4
or,-6x+5y=-2
or,5y=6x-2
or,y=.....(5)
Again (3)+(4),
4x+6y=62
or,2x+3y=31
or,2x+=31
or,=31
or,28x-6=155
or,28x=161
or,x= =5.75
By putting x= in (5) ,
y= 
or,y=
or,y=
or,y=
or,y=6.5 
So D(x,y)=(5.75,6.5)

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