What are the coordinates of the image of the point $(4, -5)$ with respect to the line $y = x$?

The equation of the line bisecting perpendicularly the segment joining the points $(-4, 6)$ and $(8, 8)$ is

If the point $P(4,1)$ undergoes a reflection in the line $x-y=0$,then a translation through a distance of $2$ units along the positive $X$-axis and finally projected on the $X$-axis,then the coordinates of $P$ in the final position are

The coordinates of the image point $Q$ of the point $P(-5, 13)$ with respect to the line $2x - 3y - 3 = 0$ are:

$A$ person standing at the junction of two straight paths represented by the equations $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ wants to reach the path whose equation is $6x - 7y + 8 = 0$ in the least time. Find the equation of the path that he should follow.

The image of the family of lines $(\lambda + 2)x + (\lambda - 1)y - (8\lambda + 1) = 0$ in the line mirror $y = x$ is (where $\lambda$ and $\mu$ are parameters):