Answer
$S=(2, -3)$.
Work Step by Step
In Example 5, it was demonstrated
that the diagonals of a parallelogram bisect each other,
meaning that they have a common midpoint.
So we search for a point $S(x, y)$ such that
the midpoints of $PR$ and of $QS$ are the same point.
$(\displaystyle \frac{4+(-1)}{2}, \displaystyle \frac{2+(-4)}{2})=(\frac{x+1}{2}, \displaystyle \frac{y+1}{2})$.
Setting the x-coordinates equal, we get
$\displaystyle \frac{4+(-1)}{2}=\frac{x+1}{2}$
$4-1=x+1$
$3-1=x$
$x=2$.
Setting the y-coordinates equal, we get
$\displaystyle \frac{2+(-4)}{2}=\frac{y+1}{2}$
$2-4=y+1$
$-2-1=y$
$y=-3$.
Thus $S=(2, -3)$.
