Answer
$\displaystyle \frac{3\sqrt{2}}{2}$
Work Step by Step
We find a point on the plane: $P(-1,0,0)$.
Given the point $S(1,0,-1)$, we have $\overrightarrow{PS}=\langle 2,0,-1 \rangle$
The vector normal to the plane is ${\bf n}=\langle -4,1,1 \rangle$
The distance of point S from the plane is given by formula (6),
d=$\displaystyle \left|\frac{ \overrightarrow{PS}\cdot{\bf n}}{|{\bf n}|}\right|=\left|\frac{-8+0-1}{\sqrt{16+1+1}}\right|=\frac{9}{3\sqrt{2}}=\frac{3\sqrt{2}}{2}$
