Question

determine whether AB and MN are parallel, perpendicular, or neither, A(-4,-8) B(4,-6) M(-3,5) N(-1,-3) A.neither B.parallel C.perpendicular

Answer 1

for this, we will find the slope of both the lines AB and MN

the slope of AB is

$\begin{gathered} m=\frac{-6-(-8)}{4-(-4)} \\ m=\frac{2}{8}=\frac{1}{4} \end{gathered}$

the slope of MN is,

$\begin{gathered} m=\frac{-3-5}{-1-(-3)} \\ m=\frac{-8}{2}=-4 \end{gathered}$

both the slopes are different, so line AB and MN is not parallel.

but

$-4\times\frac{1}{4}=-1$

the multiplication of both the slope is -1 so line AB and MN is perpendicular to each other.

option C is correct.