If A(1, 2), B(3, 4), C(5, 7) and D(x, y) are the vertices of a parallelogram ABCD, then the value of x + y is.

8

We know , midpoints of two points X and Y is ( \(\frac{ x1 + x2}{2}\) , \(\frac{ y1 + y2}{2}\) )

Mid point of AC = Mid point of BD

\(\frac{ 1 + 5}{2}\)  , \(\frac{ 2 + 7}{2}\)  = \(\frac{ 3 + x}{2}\)  , \(\frac{ 4 + y}{2}\)

3  , \(\frac{ 9}{2}\)  = \(\frac{ 3 + x}{2}\)  , \(\frac{ 4 + y}{2}\)

\(\frac{ 3 + x}{2}\) = 3  ,  \(\frac{ 4 + y}{2}\) = \(\frac{ 9}{2}\)

x = 6 - 3 = 3 , y = 5

Now, x + y = 3 + 5 = 8

The correct answer is Option (4) → 8