Suppose a triangle is formed by $x+y=10$ and the coordinate axes. Then the number of points $\left(x,y\right)$ where $x$ and $y$ are natural numbers, lying inside the triangle is

A ray of light coming from the point $(2,2\sqrt{3})$ is incident at an angle $30°$ on the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets $x$ -axis at the point $B$. Then, the line $AB$ passes through the point
 

If $\mathrm{Q}(0,-1,-3)$ is the image of the point $P$ in the plane $3x-y+4z=2$ and $R$ is the point $(3,-1,-2)$, then the area (in sq. units) of $\Delta PQR$ is