Question

$(1,2),(4,y),(x,6)$ and $(3,5)$ are the vertices of a parallelogram taken in order, $x$ and $y$ are

• A. $(3,6)$
• B. $(6,3)$
• C. $(4,9)$
• D. $(9,4)$

Answer 1

The correct option is B $(6,3)$

We are given that $A(1,2),B(4,y),C(x,6),D(3,5)$ form the vertices of the given parallelogram.

Thus, the diagonals bisect each other at the point of $P$.

By using Mid-point formula we have,

$\Rightarrow x=\left(\frac{x_1+x_2}{2}\right)andy=\left(\frac{y_1+y_2}{2}\right)$

$\Rightarrow (\frac{x+1}{2},\frac{6+2}{2})=(\frac{3+4}{2},\frac{5+y}{2})$

$\Rightarrow \frac{x+1}{2}=\frac{7}{2}\Rightarrow x+1=7$ and $\therefore x=6$

Also, $4=\frac{5+y}{2}\Rightarrow 5+y=8\therefore y=3$

Now, we have our solution $x=6$ and $y=3$.