Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Pretest: Polygons

The coordinates of the endpoints of [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are [tex]A(3,6)[/tex], [tex]B(8,7)[/tex], [tex]C(3,3)[/tex], and [tex]D(8,4)[/tex]. Which statement describes how [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are related?

A. [tex]\overline{AB} \parallel \overline{CD}[/tex]

B. [tex]\overline{AB} \perp \overline{CD}[/tex], and [tex]\overline{AB}[/tex] bisects [tex]\overline{CD}[/tex]

C. [tex]\overline{AB} \perp \overline{CD}[/tex], but [tex]\overline{AB}[/tex] does not bisect [tex]\overline{CD}[/tex]

D. [tex]\overline{AB}[/tex] is neither parallel nor perpendicular to [tex]\overline{CD}[/tex]

Sagot :

GinnyAnswer
To determine the relationship between the line segments \(\overline{A B}\) and \(\overline{C D}\), we need to analyze their slopes and respective positions. Here's a step-by-step solution:

1. Calculate the slope of \(\overline{A B}\):
- Coordinates: \(A(3,6)\) and \(B(8,7)\).
- Formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
[tex]\[ \text{slope of } \overline{A B} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
- Substituting the values:
[tex]\[ \text{slope of } \overline{A B} = \frac{7 - 6}{8 - 3} = \frac{1}{5} \][/tex]

2. Calculate the slope of \(\overline{C D}\):
- Coordinates: \(C(3,3)\) and \(D(8,4)\).
- Using the same formula:
[tex]\[ \text{slope of } \overline{C D} = \frac{4 - 3}{8 - 3} = \frac{1}{5} \][/tex]

3. Compare the slopes:
- Slope of \(\overline{A B}\) = \(\frac{1}{5}\).
- Slope of \(\overline{C D}\) = \(\frac{1}{5}\).

4. Since the slopes of \(\overline{A B}\) and \(\overline{C D}\) are equal:
- The lines are parallel if their slopes are equal.

Therefore, the correct statement is:

A. \(\overline{A B} \parallel \overline{C D}\).

So, the relationship between the segments is that [tex]\(\overline{A B}\)[/tex] is parallel to [tex]\(\overline{C D}\)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.