The point $(2,3)$ is first reflected in the straight line $y=x$ and then translated through a distance of $2$ units along the positive direction of the $X$-axis. The coordinates of the transformed point are

Let $L$ denote the line in the $xy$-plane with $x$ and $y$ intercepts as $3$ and $1$ respectively. Then the image of the point $(-1, -4)$ in this line is

If $A$ and $B$ are two points on the line $3x + 4y + 15 = 0$ such that $OA = OB = 9$ units,then the area of the triangle $OAB$ is

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

$A$ ray of light is incident along a line which meets another line,$7x - y + 1 = 0$,at the point $(0, 1)$. The ray is then reflected from this point along the line,$y + 2x = 1$. Then the equation of the line of incidence of the ray of light is

Let $L$ be the line $y = 2x$ in two dimensions.
Statement-$1$: The reflection of the point $(0, 1)$ in $L$ is the point $(4/5, 3/5)$.
Statement-$2$: The points $(0, 1)$ and $(4/5, 3/5)$ lie on opposite sides of the line $L$ and are equidistant from it.