Answer: The correct option is (B) [tex]EF=-\dfrac{2}{3},~~FG=\dfrac{3}{2}.[/tex]
Step-by-step explanation: Given that DEFG is a square in the figure shown and the slope of DE is [tex]\dfrac{3}{2}.[/tex]
We are to find the slope of EF and FG.
We know that
the adjacent sides of a square are perpendicular to each other and the opposite sides are parallel.
Also, the product of the slopes of two perpendicular lines is -1 and the slopes of two parallel lines are equal.
Since DE and EF are adjacent sides of the square DEFG, so we must have
[tex]\textup{slope of DE}\times\textup{slope of EF}=-1\\\\\\\Rightarrow \textup{slope of EF}=-\dfrac{1}{\textup{slope of DE}}=-\dfrac{1}{\frac{3}{2}}=-\dfrac{2}{3}.[/tex]
Now, DE and FG are opposite sides, so they must be parallel. So, we get
[tex]\textup{slope of FG}=\textup{slope of DE}=\dfrac{3}{2}.[/tex]
Thus, the slope of EF is [tex]-\dfrac{2}{3}[/tex] and the slope of FG is [tex]\dfrac{3}{2}.[/tex]
Option (B) is CORRECT.
