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

The distance from the origin to the image of $(1,1)$ with respect to the line $x+y+5=0$ is (in $\sqrt{2}$)

The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $y = 3x + 4$ are given by

$A$ light beam emanating from the point $A(3, 10)$ reflects from the line $2x + y - 6 = 0$ and then passes through the point $B(5, 6)$. The equations of the incident and reflected beams are respectively:

If the coordinates of the points $A, B, C$ are $(-1, 5), (0, 0)$ and $(2, 2)$ respectively and $D$ is the midpoint of $BC$,then the equation of the perpendicular drawn from $B$ to the line $AD$ is

The image of a point $A(3, 8)$ in the line $x + 3y - 7 = 0$ is