Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$
$L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$
A) parallel
B) perpendicular
C) neither

Question

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$ 
$L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$
A) parallel
B) perpendicular
C) neither

Quizplus · Accepted Answer

First, let's find the slope of each line:

$L _ { 1 } = \frac{-6-1}{-1-(-1)} = -\frac{7}{2}$

$L _ { 2 } = \frac{-8-(-8)}{24-3}=0$

Since the slope of $L _ { 2 }$ is zero, it is a horizontal line. Any line perpendicular to a horizontal line must be a vertical line. Therefore, we can see that the slope of $L _ { 1 }$ is undefined, meaning that it is a vertical line.

A vertical line and a horizontal line are always perpendicular, so the answer is B (perpendicular).

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