Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( 7 , - 4 ) , ( - 9 , - 1 )$ $L _ { 2 } : ( 4 , - 6 ) , ( - 3,9 )$
A) parallel
B) perpendicular
C) neither

Question

Quizplus · Accepted Answer

The slope of $L_1$ is calculated using the points $(7, -4)$ and $(-9, -1)$ as $\frac{-1 - (-4)}{-9 - 7} = \frac{3}{-16}$. The slope of $L_2$ using the points $(4, -6)$ and $(-3, 9)$ is $\frac{9 - (-6)}{-3 - 4} = \frac{15}{-7}$. Since the slopes are not negative reciprocals of each other, the lines are not perpendicular. Also, since the slopes are not equal, the lines are not parallel. Therefore, the lines are neither parallel nor perpendicular.

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