Question:
Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at $(2,4)$, then one of its vertex is :
Correct Option: , 4
Solution:
$\frac{x_{1}+0}{2}=2 ; \quad x_{i}=4 \quad$ similarly $\quad y_{1}=5$
$\mathrm{C} \Rightarrow(4,5)$
Now equation of $B C$ is $x-y=-1$
and equation of CD is $x+y=9$
Solving $x+y=9$ and $x-y=-3$
Point $\mathrm{D}$ is $(3,6)$
Option (4)