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

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:

The image of the point $(4, -3)$ with respect to the line $y = x$ is

Let $M$ be the foot of the perpendicular drawn from the point $(5, -7)$ to the line $3x - 5y + 1 = 0$. Then the perpendicular distance from $M$ to the line $2x + 5y - 3 = 0$ is

Find the equation of the line perpendicular to the line $ax + by + c = 0$ and passing through the point $(a, b)$.

Let $L$ denote the line in the $xy$-plane with $x$ and $y$ intercepts as $3$ and $1$ respectively. Then the image of the point $(-1, -4)$ in this line is