Answer
$S$ must be located at $(0, -4)$.
Area = $50$.
Work Step by Step
See sketch.
The point $S$ must be located at $(0, -4)$.
To find the area,
we find the length of one side and square it.
$d(Q, R)=\sqrt{(-5-0)^{2}+(1-6)^{2}}=\sqrt{(-5)^{2}+(-5)^{2}}$
$=\sqrt{25+25}=\sqrt{50}$
$A= (\sqrt{50})^{2}=50$.
