Question

1. p(12, -2), q(5, -10), r(-4, 10), s(4, 3)

slope of (overline{pq})
slope of (overline{rs})
types of lines

Explanation:

Step1: Calculate slope of $\overline{PQ}$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
For $P(12,-2), Q(5,-10)$:
$m_{PQ}=\frac{-10-(-2)}{5-12}=\frac{-8}{-7}=\frac{8}{7}$

Step2: Calculate slope of $\overline{RS}$

For $R(-4,10), S(4,3)$:
$m_{RS}=\frac{3-10}{4-(-4)}=\frac{-7}{8}$

Step3: Classify line relationship

Check if slopes are negative reciprocals: $m_{PQ} \times m_{RS} = \frac{8}{7} \times \frac{-7}{8} = -1$
When product of slopes is -1, lines are perpendicular.

Answer:

Category	Result
Slope of $\overline{RS}$	$-\frac{7}{8}$
Types of Lines	Perpendicular