Question

the coordinates of the endpoints of $overline{ab}$ and $overline{cd}$ are $a(3, 6)$, $b(8, 7)$, $c(3, 3)$, and $d(8, 4)$. which statement describes how $overline{ab}$ and $overline{cd}$ are related?
a. $overline{ab} \parallel \overline{cd}$
b. $overline{ab} \perp \overline{cd}$, and $overline{ab}$ bisects $overline{cd}$.
c. $overline{ab} \perp \overline{cd}$, but $overline{ab}$ does not bisect $overline{cd}$.
d. $overline{ab}$ is neither parallel nor perpendicular to $overline{cd}$.

Explanation:

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

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m_{AB} = \frac{7 - 6}{8 - 3} = \frac{1}{5}$

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

$m_{CD} = \frac{4 - 3}{8 - 3} = \frac{1}{5}$

Step3: Check parallel/perpendicular rules

Parallel lines have equal slopes; perpendicular lines have slopes whose product is $-1$.
$m_{AB} = m_{CD} = \frac{1}{5}$, so $\overline{AB} \parallel \overline{CD}$

Answer:

A. $\overline{AB} \parallel \overline{CD}$