Question

The vertices of a parallelogram are (1, 3), (4, y), (x, 6) and (2, 5). Find the values of x and y.

• A. x = 5, y = 4
• B. x = 2, y = 6
• C. x = 3, y = 5
• D. x = 3, y = 4

Answer 1

The correct option is A x = 5, y = 4


The given points are : A(1, 3), B(4, y), C(x, 6), and D(2, 5).
Since, the diagonals of a parallelogram bisect each other.
$\therefore$ The coordinates of P are:
$X=\frac{x+1}{2}=\frac{4+2}{2}\Rightarrow x+1=6\Rightarrow x=5Y=\frac{5+y}{2}=\frac{6+3}{2}\Rightarrow 5+y=9\Rightarrow y=4$
$\therefore$ The required values of x and y are:
$x=5,y=4$.