Question

determine if $overline{ab}$ and $overline{cd}$ are parallel, perpendicular, or neither.

1. $a(-11, 5)$, $b(-8, 4)$, $c(8, -7)$, $d(-1, -4)$
2. $a(-3, 8)$, $b(1, 15)$, $c(10, -9)$, $d(3, -5)$
3. $a(9, -3)$, $b(9, 4)$, $c(-2, 10)$, $d(-2, 6)$

Explanation:

Problem 22:

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

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For $A(-3,8)$ and $B(1,15)$:
$m(\overline{AB}) = \frac{15 - 8}{1 - (-3)} = \frac{7}{4}$

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

For $C(10,-9)$ and $D(3,-5)$:
$m(\overline{CD}) = \frac{-5 - (-9)}{3 - 10} = \frac{4}{-7} = -\frac{4}{7}$

Step3: Determine line type

Check if slopes are equal (parallel) or negative reciprocals (perpendicular). $\frac{7}{4}$ and $-\frac{4}{7}$ are negative reciprocals ($\frac{7}{4} \times (-\frac{4}{7}) = -1$), so lines are perpendicular.

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

For $A(9,-3)$ and $B(9,4)$: $x$-coordinates are equal ($9 = 9$), so slope is undefined (vertical line).

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

For $C(-2,10)$ and $D(-2,6)$: $x$-coordinates are equal ($-2 = -2$), so slope is undefined (vertical line).

Step3: Determine line type

Both slopes are undefined (vertical lines), so they are parallel.

Answer:

$m(\overline{AB})$	$m(\overline{CD})$	Types of Lines

Problem 23: