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

$A$ straight line $L_1$ passing through $A(3,1)$ meets the coordinate axes at $P$ and $Q$ such that its distance from the origin $O$ is maximum. Then the area of $\triangle OPQ$ is (in sq. units):

The perpendicular from the origin to the line $y=mx+c$ meets it at the point $(-1, 2)$. Find the values of $m$ and $c$.

If $Q$ and $R$ are the images of the point $P(2,3)$ with respect to the lines $x-y+2=0$ and $2x+y-2=0$ respectively,then $Q$ and $R$ lie on

$A(-1, 1)$ and $B(5, 3)$ are opposite vertices of a square in the $xy$-plane. The equation of the other diagonal (not passing through $A$ and $B$) of the square is given by:

The equation of the straight line passing through the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$ and perpendicular to the line $3x - 5y + 11 = 0$ is