Find the equation of the perpendicular bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.

The point $Q$ is the image of the point $P(1,5)$ about the line $y=x$ and $R$ is the image of the point $Q$ about the line $y=-x$. The circumcentre of the $\Delta PQR$ is

Find the coordinates of the foot of the perpendicular drawn from the point $(0, 5)$ to the line $3x - 4y - 5 = 0$.

The length of the perpendicular from the origin,on the normal to the curve $x^{2}+2xy-3y^{2}=0$ at the point $(2,2)$ is

$A$ light ray emits from the origin making an angle $30^{\circ}$ with the positive $x$-axis. After getting reflected by the line $x + y = 1$,if this ray intersects the $x$-axis at $Q$,then the abscissa of $Q$ is

The area (in square units) of the quadrilateral formed by the point of intersection of the lines $x+y-1=0$ and $x-y+1=0$,the point $P(1,1)$,and the feet of the perpendiculars from this point onto the lines is: