The slope of segment QV is given by
[tex] m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_v-y_q}{x_v-x_q} = \dfrac{-1-2}{2-(-4)} = \dfrac{-3}{6} = -\dfrac{1}{2} [/tex]
Now, given a line [tex] r [/tex] with a certain slope [tex] m [/tex], all lines perpendicular to [tex] r [/tex] have slope [tex]m'[/tex] such that
[tex] mm' = -1 \iff m'=-\dfrac{1}{m}[/tex]
So, in your case, you have
[tex] m' = -\dfrac{1}{-\frac{1}{2}} = 2 [/tex]
