The coordinates of the image point $Q$ of the point $P(-5, 13)$ with respect to the line $2x - 3y - 3 = 0$ are:

Let $A \left(\frac{3}{\sqrt{a}}, \sqrt{a}\right)$ with $a > 0$ be a fixed point in the $xy$-plane. The image of $A$ in the $y$-axis is $B$,and the image of $B$ in the $x$-axis is $C$. If $D(3 \cos \theta, a \sin \theta)$ is a point in the fourth quadrant such that the maximum area of $\triangle ACD$ is $12$ square units,then $a$ is equal to:

If the perpendicular drawn from the point $(2, -3)$ to the straight line $4x - 3y + 8 = 0$ meets it at $M(a, b)$ and $a^3 - b^3 = k^3$,then $k=$

If the image of the point $(3, 8)$ in the line $x + 3y = 7$ is $(\alpha, \beta)$,then $\alpha + \beta =$

The image of a point $A(3, 8)$ in the line $x + 3y - 7 = 0$ is

Find the image of the point $(3,8)$ with respect to the line $x+3y=7$,assuming the line to be a plane mirror.