To determine which sentence about the points is true, we need to analyze the slopes of the lines formed by these points. Let's start by considering the lines [tex]\(\overleftrightarrow{AB}\)[/tex] and [tex]\(\overleftrightarrow{CD}\)[/tex].
1. Calculate the slope of line [tex]\(\overleftrightarrow{AB}\)[/tex]:
[tex]\[
\text{slope}_{AB} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{-2 - (-8)} = \frac{3}{6} = 0.5
\][/tex]
2. Calculate the slope of line [tex]\(\overleftrightarrow{CD}\)[/tex]:
[tex]\[
\text{slope}_{CD} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-1)}{-6 - (-3)} = \frac{6}{-3} = -2.0
\][/tex]
3. Determine if the lines are parallel:
Lines are parallel if their slopes are equal. Here, [tex]\(\text{slope}_{AB} = 0.5\)[/tex] and [tex]\(\text{slope}_{CD} = -2.0\)[/tex]. Since [tex]\(0.5 \ne -2.0\)[/tex], [tex]\(\overleftrightarrow{AB}\)[/tex] and [tex]\(\overleftrightarrow{CD}\)[/tex] are not parallel.
4. Determine if the lines are perpendicular:
Lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex]. We calculate:
[tex]\[
\text{slope}_{AB} \times \text{slope}_{CD} = 0.5 \times (-2.0) = -1.0
\][/tex]
Since the product indeed equals [tex]\(-1.0\)[/tex], [tex]\(\overleftrightarrow{AB}\)[/tex] and [tex]\(\overleftrightarrow{CD}\)[/tex] are perpendicular.
Conclusively, the correct answer is:
B. [tex]\( \overleftrightarrow{AB}\)[/tex] and [tex]\( \overleftrightarrow{CD}\)[/tex] are perpendicular lines.
