The opposite vertices of a square are $(1, 2)$ and $(3, 8)$, then the equation of a diagonal of the square passing through the point $(1, 2)$, is
$3x - y - 1 = 0$
$3y - x - 1 = 0$
$3x + y + 1 = 0$
None of these
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 :
The co-ordinates of the orthocentre of the triangle bounded by the lines, $4x - 7y + 10 = 0; x + y=5$ and $7x + 4y = 15$ is :
The diagonals of the parallelogram whose sides are $lx + my + n = 0,$ $lx + my + n' = 0$,$mx + ly + n = 0$, $mx + ly + n' = 0$ include an angle
Show that the area of the triangle formed by the lines
$y=m_{1} x+c_{1}, y=m_{2} x+c_{2}$ and $x=0$ is $\frac{\left(c_{1}-c_{2}\right)^{2}}{2\left|m_{1}-m_{2}\right|}$.
If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are