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

If the perpendicular bisector of the line segment joining $P(1, 4)$ and $Q(k, 3)$ has a $y$-intercept of $-4$,then the possible value of $k$ is:

If a ray travels along the line $x = 1$ and gets reflected by the line $x + y = 1$,find the equation of the reflected ray.

The reflection of the point $(1, 1)$ along the line $y = -x$ is

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.

The point $(2,3)$ is first reflected in the straight line $y=x$ and then translated through a distance of $2$ units along the positive direction of the $X$-axis. The coordinates of the transformed point are