$A$ ray of light coming from the point $P(1, 2)$ gets reflected from the point $Q$ on the $x$-axis and then passes through the point $R(4, 3)$. If the point $S(h, k)$ is such that $PQRS$ is a parallelogram,then $hk^2$ is equal to :

Three points are $A(6, 3)$,$B(-3, 5)$,and $C(4, -2)$. If $P(x, y)$ is a point,then the ratio of the area of $\Delta PBC$ to the area of $\Delta ABC$ is:

Two sides of a rhombus are along the lines $x-y+1=0$ and $7x-y-5=0$. If its diagonals intersect at $(-1,-2)$,then one of the vertices of this rhombus is

Let $\alpha, \beta, \gamma, \delta \in \mathbb{Z}$ and let $A(\alpha, \beta), B(1, 0), C(\gamma, \delta)$ and $D(1, 2)$ be the vertices of a parallelogram $ABCD$. If $AB = \sqrt{10}$ and the points $A$ and $C$ lie on the line $3y = 2x + 1$,then $2(\alpha + \beta + \gamma + \delta)$ is equal to

The length of the altitude through $A$ of the triangle $ABC$,where $A \equiv (-3, 0)$,$B \equiv (4, -1)$,and $C \equiv (5, 2)$,is

$x+8y-22=0$,$5x+2y-34=0$,and $2x-3y+13=0$ are the three sides of a triangle. The area of the triangle is