Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0.$ If the equation to one diagonal is $11x + 7y = 9,$ then the equation of the other diagonal is

One side of a square is inclined at an acute angle $\alpha$ with the positive $x-$axis,and one of its extremities is at the origin. If the remaining three vertices of the square lie above the $x-$axis and the side of a square is $4$,then the equation of the diagonal of the square which is not passing through the origin is

The area of the triangle formed by the lines $7x - 2y + 10 = 0$,$7x + 2y - 10 = 0$ and $y + 2 = 0$ is ............ $sq. \, units$.

The area of a triangle is $5$ and two of its vertices are $A(2, 1)$ and $B(3, -2)$. The third vertex,which lies on the line $y = x + 3$,is:

If $x_1, x_2, x_3$ and $y_1, y_2, y_3$ are in $G.P.$ with the same common ratio,then the points $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are:

In a $\triangle ABC$,medians $AD$ and $BE$ are drawn. If $AD = 4$,$\angle DAB = \frac{\pi}{6}$,and $\angle ABE = \frac{\pi}{3}$,then the area of the $\triangle ABC$ is