The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ 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 $\triangle PQR$).
$I$. $[BCX] = [BCY]$
$II$. $[ACX] \cdot [ABY] = [AXY] \cdot [ABC]$

If the incentre of the triangle formed by the lines $x-2=0$,$x+y-1=0$,and $x-y+3=0$ is $(\alpha, \beta)$,then $\beta=$

If a vertex of an equilateral triangle is at the origin and the second vertex is $(4, 0)$,then its third vertex is

If a straight line $L$ is perpendicular to the line $4x - 2y = 1$ and forms a triangle of area $4 \text{ sq unit}$ with the coordinate axes,then the equation of the line $L$ is

The area of the quadrilateral formed by the lines $x+2y+3=0$,$2x+4y+9=0$,$x-2y+3=0$,and $3x-6y+11=0$ is