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.
Answer & explanation
Correct answer: option 4
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