If $ad-bc \neq 0$,then the area (in sq. units) of the parallelogram formed by the lines $ax+by+2=0$,$ax+by+5=0$,$cx+dy+3=0$ and $cx+dy+7=0$ is

The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$. If the third side passes through the point $(1, -10)$,then the equation of the third side is:

The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4x + y = 14$ and $3x - 2y = 5$,respectively. The point $\left(2, -\frac{4}{3}\right)$ divides the third side $BC$ internally in the ratio $2:1$. The equation of the side $BC$ is:

Find the equation of a line parallel to $2x - 3y = 4$ which forms a triangle of area $12$ square units with the coordinate axes.

In a $\triangle ABC$,$AB = AC = 37$. Let $D$ be a point on $BC$ such that $BD = 7$ and $AD = 33$. The length of $CD$ is:

In a $\triangle ABC$,points $X$ and $Y$ are on $AB$ and $AC$,respectively,such that $XY$ is parallel to $BC$. Which of the two following equalities always hold? (Here $[PQR]$ denotes the area of $\triangle PQR$).
$I$. $[BCX] = [BCY]$
$II$. $[ACX] \cdot [ABY] = [AXY] \cdot [ABC]$