The vertex of an equilateral triangle is $(2,-1)$ and the equation of its base in $x + 2y = 1$. The length of its sides is
$4/\sqrt {15} $
$2/\sqrt {15} $
$4/3\sqrt 3 $
$1/\sqrt 5 $
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
A vertex of square is $(3, 4)$ and diagonal $x + 2y = 1,$ then the second diagonal which passes through given vertex will be
Let the points of intersections of the lines $x-y+1=0$, $x-2 y+3=0$ and $2 x-5 y+11=0$ are the mid points of the sides of a triangle $A B C$. Then the area of the triangle $\mathrm{ABC}$ is .... .
The triangle formed by the lines $x + y - 4 = 0,\,$ $3x + y = 4,$ $x + 3y = 4$ is
The area of triangle formed by the lines $x + y - 3 = 0 , x - 3y + 9 = 0$ and $3x - 2y + 1= 0$