QJEEM21Maa481: JEE Main 2021 Mathematics - Class 11 JEEM21Maa481 Solution: Two sides of a parallelogram are along the lines 4x + 5y = 0…

Both the lines pass through origin.



point D is equal to intersection of 4x + 5y = 0 & 11x + 7y = 9

So, coordinates of point $D = \left( {{5 \over 3}, - {4 \over 3}} \right)$

Also, point B is point of intersection of 7x + 2y = 0 and 11x + 7y = 9

So, coordinates of point $B = \left( { - {2 \over 3},{7 \over 3}} \right)$

diagonals of parallelogram intersect at middle let middle point of B, D

$\Rightarrow \left( {{{{5 \over 3} - {2 \over 3}} \over 2},{{{{ - 4} \over 3} + {7 \over 3}} \over 2}} \right) = \left( {{1 \over 2},{1 \over 2}} \right)$

equation of diagonal AC

$\Rightarrow (y - 0) = {{{1 \over \alpha } - 0} \over {{1 \over \alpha } - 0}}(x - 0)$

$y = x$

diagonal AC passes through (2, 2)