Question

pq and rs are parallel, perpendicular, or neither. 2. p(-3, 14), q(2, -1), r(4, 8), s(-2, -10)
| $m\left(\overline{pq}\
ight)$ | $m\left(\overline{rs}\
ight)$ | types of lines |

Explanation:

Step1: Calculate slope of PQ

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For $P(-3, 14)$ and $Q(2, -1)$:
$m_{PQ} = \frac{-1 - 14}{2 - (-3)} = \frac{-15}{5} = -3$

Step2: Calculate slope of RS

For $R(4, 8)$ and $S(-2, -10)$:
$m_{RS} = \frac{-10 - 8}{-2 - 4} = \frac{-18}{-6} = 3$

Step3: Determine line type

Parallel lines have equal slopes, perpendicular lines have slopes that are negative reciprocals (product = -1). Here, $-3
eq 3$ and $(-3)(3) = -9
eq -1$, so neither.

Answer:

$m(\overline{PQ})$	$m(\overline{RS})$	Types of Lines