To determine the relationship between the lines \( \overline{AB} \) and \( \overline{CD} \), let's analyze their slopes and other properties in a step-by-step manner:
1. Calculate the slope of \( \overline{AB} \):
The slope \( m_{AB} \) is calculated using the formula:
[tex]\[
m_{AB} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, \( A = (3, 6) \) and \( B = (8, 7) \).
So,
[tex]\[
m_{AB} = \frac{7 - 6}{8 - 3} = \frac{1}{5}
\][/tex]
2. Calculate the slope of \( \overline{CD} \):
The slope \( m_{CD} \) is calculated using the same slope formula:
[tex]\[
m_{CD} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, \( C = (3, 3) \) and \( D = (8, 4) \).
So,
[tex]\[
m_{CD} = \frac{4 - 3}{8 - 3} = \frac{1}{5}
\][/tex]
3. Compare the slopes of \( \overline{AB} \) and \( \overline{CD} \):
Since both slopes are equal, \( m_{AB} = m_{CD} = \frac{1}{5} \), this implies that the lines \( \overline{AB} \) and \( \overline{CD} \) are parallel.
4. Conclusion:
Since the slopes are equal, the correct statement is:
[tex]\[
\overline{A B} \parallel \overline{C D}
\][/tex]
Thus, the correct answer is:
A. [tex]\( \overline{A B} \| \overline{C D} \)[/tex]
