Question

I need help with this math question

Answer 1

The slope of segment QV is given by

$m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_v-y_q}{x_v-x_q} = \dfrac{-1-2}{2-(-4)} = \dfrac{-3}{6} = -\dfrac{1}{2}$

Now, given a line $r$ with a certain slope $m$, all lines perpendicular to $r$ have slope $m'$ such that

$mm' = -1 \iff m'=-\dfrac{1}{m}$

So, in your case, you have

$m' = -\dfrac{1}{-\frac{1}{2}} = 2$