The equation to the sides of a triangle are $x – 3y = 0$, $4x + 3y = 5$ and $3x + y = 0$. The line $3x – 4y = 0$ passes through

Let a triangle be bounded by the lines $L _{1}: 2 x +5 y =10$; $L _{2}:-4 x +3 y =12$ and the line $L _{3}$, which passes through the point $P (2,3)$, intersect $L _{2}$ at $A$ and $L _{1}$ at $B$. If the point $P$ divides the line-segment $A B$, internally in the ratio $1: 3$, then the area of the triangle is equal to

If $A$ is $(2, 5)$, $B$ is $(4, -11)$ and $ C$ lies on $9x + 7y + 4 = 0$, then the locus of the centroid of the $\Delta ABC$ is a straight line parallel to the straight line is

The sides of a rhombus $ABCD$ are parallel to the lines, $x – y + 2\, = 0$ and $7x – y + 3\, = 0$. If the diagonals of the rhombus intersect at $P( 1, 2)$ and the vertex $A$ ( different from the origin) is on the $y$ axis, then the ordinate of $A$ is

If the straight lines $x + 3y = 4,\,\,3x + y = 4$ and $x +y = 0$ form a triangle, then the triangle is