Length of the Perpendicular from a Point to a Line

Show that the distance of the point $(6,-2)$ from the line $4x+3y=12$ is half the distance of the point $(3,4)$ from the line $4x-3y=12$.

Find the length of the perpendicular drawn from the point $\left(0,0\right)$ against the straight line $x-3y-4=0$.

Find the length of the perpendicular drawn from the point $\left(3,4\right)$ against the straight line $3x-4y+10=0$.      [Enter the value excluding units]

A straight line through $P(3,4)$ makes an angle of $60°$ with the positive direction of the $X-$axis. Find the coordinates of the points on the line which are $5$ units away from $P$.

Find the point on the straight line $3x+y+4=0$ which is equidistant from the points $(-5,6)$ and $(3,2)$.

Find the set of values of $a$ if the points $(1,2)$ and $(3,4)$ lie to the same side of the straight line $3x-5y+a=0$.