The locus of the mid-points of the perpendiculars drawn from points on the line, $\mathrm{x}=2 \mathrm{y}$ to the line $\mathrm{x}=\mathrm{y}$ is
$2 x-3 y=0$
$7 x-5 y=0$
$5 x-7 y=0$
$3 x-2 y=0$
If the co-ordinates of the middle point of the portion of a line intercepted between coordinate axes $(3,2)$, then the equation of the line will be
The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$ and the third side passes through the point $(1, -10)$. The equation of the third side is
Show that the path of a moving point such that its distances from two lines $3 x-2 y=5$ and $3 x+2 y=5$ are equal is a straight line.
In a triangle $ABC,$ side $AB$ has the equation $2 x + 3 y = 29$ and the side $AC$ has the equation , $x + 2 y = 16$ . If the mid - point of $BC$ is $(5, 6)$ then the equation of $BC$ is :