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

$A$ ray of light passing through the point $P(2, 3)$ reflects on the $x$-axis at point $A$ and the reflected ray passes through the point $Q(5, 4)$. Let $R$ be the point that divides the line segment $AQ$ internally in the ratio $2:1$. Let the coordinates of the foot of the perpendicular $M$ from $R$ on the bisector of the angle $PAQ$ be $(\alpha, \beta)$. Then,the value of $7\alpha + 3\beta$ is equal to.......

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.

Sum of values of $k$ for which the image of the point $(\lambda^2 + 1, \lambda)$ with respect to the line $y = -3x + 6k$ is the point $(\lambda, \lambda - 1)$ is:

If $A(2, -1)$ and $B(6, 5)$ are two points,the ratio in which the foot of the perpendicular from $P(4, 1)$ to $AB$ divides $AB$ is:

If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to the line $L = 0$,then $L$ is equal to