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

Let $L$ be the line $y = 2x$ in the two-dimensional plane.
Statement $1$: The image of the point $(0, 1)$ in $L$ is the point $\left( \frac{4}{5}, \frac{3}{5} \right)$.
Statement $2$: The points $(0, 1)$ and $\left( \frac{4}{5}, \frac{3}{5} \right)$ lie on opposite sides of the line $L$ and are at equal distance from it.

$A$ light ray along the line $x + \sqrt{3}y = \sqrt{3}$ reaches the $x$-axis and gets reflected. Find the equation of the reflected ray.

Let a ray of light passing through the point $(3,10)$ reflect on the line $2x+y=6$ and the reflected ray pass through the point $(7,2)$. If the equation of the incident ray is $ax+by+1=0$,then $a^2+b^2+3ab$ is equal to:

The equation of the straight line passing through the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$ and perpendicular to the line $3x - 5y + 11 = 0$ is

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