Answer
a) The point $S$ must be located at (3, 6). See the graph.
b) $A_{square}=18$ units
Work Step by Step
a) The diagonals between opposite corners must have equal distances to form a square. The distance between $P(0,3)$ and $R(6,3)$ is $6$ units. Therefore, the point S must be $6$ units from the point $Q$ and equidistant from $P$ and $R$. Any point on the line $x=3$ is equidistant from $P$ and $R$. So, the point $S$ must be located at (3, 6).
b) Since the area of a square is $A_{square}=s^2$, we'll just need to find one of the lengths of its sides. To do so, we'll use the distance formula $d=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$ , using any two consecutive points. In this case, we'll use $P(0,3)$ and $Q(3,0)$
$d=\sqrt{(0-3)^2+(3-0)^2}$
$d=\sqrt{9+9}$
$d=\sqrt{18}$
Now we can find the area:
$A_{square}=(\sqrt{18})^2=18$ units
