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 given points are : A(1,2), B(4, y), C(x, 6), and D(3,5)
Since, the diagonals of a parallelogram bisect each other.
$\therefore$ The coordinates of P are:
$X=\frac{x+1}{2}=\frac{3+4}{2}\Rightarrow x+1=7\Rightarrow x=6Y=\frac{5+y}{2}=\frac{6+2}{2}\Rightarrow 5+y=8\Rightarrow y=3$
$\therefore$ The required values of x and y are:
$x=6,y=3$.