Question

if (1,2) , (4,y) ,(x , 6) and (3,5) are the vertices of a parallelogram taken in order . find x and y ?

Answer 1

the diagonal of a parallelogram bisect each other
therefore
(1+x/2,2+6/2)=(4+3/2 , y+5/2)
(1+x/2 , 4)=(7/2 , y+5/2)
Now
x=6
y=3

Answer 2

A(1,2) B(4,y) C(x,6) D(3,5)
are the vertices of a parallelogram,
then AC & BD will be diagonal of the parallelogram

Diagonal of a parallelogram bisects each other.
Let the point where the diagonals intersect each other be P

P = {(1+x)/2 , (6+2)/2} = {(4+3)/2,(y+5)/2}

(x+1)/2 = (4+3)/2
x = 6

(6+2)/2 = (y+5)/2
y = 3

hence the value of x=6 & y=3