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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2019Straight Lines

Solution:

$\frac{x_{1}+0}{2} =2; x_{i} = 4$ similarly $ y_{1}=5 $
$ C \Rightarrow \left(4,5\right) $
Now equation of $BC$ is $x - y = -1$
and equation of $CD$ is $x + y = 9$
Solving $x + y = 9$ and $x - y = -3$
Point $D$ is $(3, 6)$

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