Determine whether the line through the points $P ( 40,18 ) , Q ( 26,20 )$ and the line through $R ( 20,9 )$, $S ( 13,10 )$ are parallel, perpendicular, or neither.
A) neither
B) perpendicular
C) parallel

Question

Quizplus · Accepted Answer

The slope of the line passing through points P and Q is:

$m_1 =\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{20-18}{26-40}=\dfrac{-1}{7}$

The slope of the line passing through points R and S is:

$m_2 =\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{10-9}{13-20}=\dfrac{1}{7}$

Since the slopes of the two lines are negative reciprocals of each other, they are parallel. Therefore, the answer is C) parallel.

Determine Whether the Line Through the Points P(40,18),Q(26,20)P ( 40,18 ) , Q ( 26,20 )P(40,18),Q(26,20)

Determine Whether the Line Through the Points $P ( 40,18 ) , Q ( 26,20 )$