Take the basic concept of a parallelogram...

=> Diagonals of a ||gm bisect each other...
hence, mid point of both the diagonal is equal.

=> For x cordinate of mid-point ,
(X + m ) / 2 = (1 + 4)/2

=> For ycordinate of mid-point ,
(Y+ n) / 2 = (1 + 4)/2

Earlier, trying to solve this question in the stipulated time, I had thought of the long solution only...taking the slope of parallel rows to be equal....that would involve solving the equations...

but as you asked for a short solution... I thought a bit..and it striked.

ANSWER : E

Diagonals of a parallelogram bisect eachother

Hence midpoint of a diagonal is 4+1/2 , 4+1/2 =(2.5, 2.5)

let A(x,y)

therefore, x+m/2 = 2.5 i.e x = 5-m
similarly for y=5-n

I hope this explains.

my approach is
since it's a parallelogram the length of line bet (m,n) and (4,4) is equal to length of line between (1,1) and A
so let A's coordinate be (x,y)
so x-1 = 4-m => x=4-m
y-1 = 4-n => y=4-n