Question

use the slope to determine if lines pq and rs are parallel, perpendicular, or neither. show your work for full credit. 8. p(-4,17),q(1,-3),r(-9,3),s(-5,-4)

Explanation:

Step1: Recall slope - formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of line PQ

For points $P(-4,17)$ and $Q(1, - 3)$, we have $x_1=-4,y_1 = 17,x_2 = 1,y_2=-3$. Then $m_{PQ}=\frac{-3 - 17}{1-(-4)}=\frac{-20}{5}=-4$.

Step3: Calculate slope of line RS

For points $R(-9,3)$ and $S(-5,-4)$, we have $x_1=-9,y_1 = 3,x_2=-5,y_2=-4$. Then $m_{RS}=\frac{-4 - 3}{-5-(-9)}=\frac{-7}{4}$.

Step4: Check the relationship

Two lines are parallel if $m_1=m_2$, and perpendicular if $m_1\times m_2=-1$. Here, $m_{PQ}
eq m_{RS}$ and $m_{PQ}\times m_{RS}=(-4)\times(-\frac{7}{4}) = 7
eq - 1$.

Answer:

Neither