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?

\\(\overline{ab} \parallel \overline{cd}\\)

\\(\overline{ab} \perp \overline{cd}\\), and \\(\overline{ab}\\) bisects \\(\overline{cd}\\).

\\(\overline{ab} \perp \overline{cd}\\), but \\(\overline{ab}\\) does not bisect \\(\overline{cd}\\).

\\(\overline{ab}\\) is neither parallel nor perpendicular to \\(\overline{cd}\\).

Explanation:

⚡ Using what you learned: parallel and perpendicular lines_equations · Midpoint Formula

Step 1: Calculate slopes

Find the slopes of \(\overline{AB}\) and \(\overline{CD}\) to check for parallel or perpendicular relationships.

$$ m_{AB} = \frac{7 - 6}{8 - 3} = \frac{1}{5} $$

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

Since \(m_{AB} = m_{CD}\), the segments \(\overline{AB}\) and \(\overline{CD}\) are parallel (\(\overline{AB} \parallel \overline{CD}\)).

Answer:

\(\overline{AB} \parallel \overline{CD}\)