Question

1. p(-4, 17), q(1, -3), r(-9, 3), s(-5, 4)

table with columns: ( mleft(overline{pq}
ight) ), ( mleft(overline{rs}
ight) ), types of lines

Explanation:

Step1: Calculate slope of \( \overline{PQ} \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For \( P(-4, 17) \) and \( Q(1, -3) \), \( x_1=-4, y_1=17, x_2=1, y_2=-3 \).
\( m(\overline{PQ}) = \frac{-3 - 17}{1 - (-4)} = \frac{-20}{5} = -4 \)

Step2: Calculate slope of \( \overline{RS} \)

For \( R(-9, 3) \) and \( S(-5, 4) \), \( x_1=-9, y_1=3, x_2=-5, y_2=4 \).
\( m(\overline{RS}) = \frac{4 - 3}{-5 - (-9)} = \frac{1}{4} \)

Step3: Determine line type

Since \( -4
eq \frac{1}{4} \) (not parallel) and \( -4 \times \frac{1}{4} = -1 \) (perpendicular), they are perpendicular.

Answer:

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