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

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

The equation of the straight line which passes through the point $(a \cos^{3} \theta, a \sin^{3} \theta)$ and is perpendicular to $x \sec \theta + y \operatorname{cosec} \theta = a$ is

Let $\alpha$ and $\beta$ be integers satisfying $0 < \beta < \alpha$. Let $P(\alpha, \beta)$ be a point. Let $Q$ be the reflection of $P$ in the line $y = x$,$R$ be the reflection of $Q$ in the $y$-axis,$S$ be the reflection of $R$ in the $x$-axis,and $T$ be the reflection of $S$ in the $y$-axis. If the area of the convex pentagon $PQRST$ is $187 \ sq. \ units$,then the value of $\alpha + \beta^2$ is:

If $(h, k)$ is the image of the point $(2, -3)$ with respect to the line $5x - 3y = 2$,then $h + k =$

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