Find the coordinates of the foot of the perpendicular drawn from the point $(0, 5)$ to the line $3x - 4y - 5 = 0$.

$A$ 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:

Let $L$ be the line $y = 2x$ in two dimensions.
Statement-$1$: The reflection of the point $(0, 1)$ in $L$ is the point $(4/5, 3/5)$.
Statement-$2$: The points $(0, 1)$ and $(4/5, 3/5)$ lie on opposite sides of the line $L$ and are equidistant from it.

Find the equation of the perpendicular bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.

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):

The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is