If the perpendicular bisector of the line segment joining the points $P(1, 4)$ and $Q(k, 3)$ has a $y$-intercept equal to $-4$,then a value of $k$ is

The image of $A(1, -2)$ with respect to the straight line $L \equiv 2x - 3y + 5 = 0$ is $B$. The foot of the perpendicular from $P(-4, -1)$ onto the line joining $AB$ is:

The image of the point $P(3, 8)$ with respect to the line $x + 3y = 7$,assuming the line to be a plane mirror,is equal to .........

If the coordinates of $A$ and $B$ are $(1, 1)$ and $(5, 7)$,then the equation of the perpendicular bisector of the line segment $AB$ is

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

Let the mirror image of point $A(1, 4)$ in the line $y = x$ be point $B$; the mirror image of point $B$ in the line $y = -x$ be $C$; and the mirror image of $C$ in the $x$-axis be $D$. Then,the area of triangle $ABD$ is ............... $sq. \, units$.