Respuesta :
the lines are not parallel,and the lines are not perpendicular
Explanation
Step 1
find the slopes
when you have two points of a line P1 and P2 you can find the slope using
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]for segment AB
P1(5,6)
P2(2,2)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope1}=\frac{2-6}{2-5}=\frac{-4}{-3}=\frac{4}{3} \end{gathered}[/tex]for segment CD
P1(-4,-9)
P2(-8,2)
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{2-(-9)}{-8-(-4)}=\frac{2+9}{-8+4}=\frac{11}{-4}=\frac{-11}{4} \end{gathered}[/tex]Step 2
compare the slopes
[tex]\begin{gathered} \text{if slope1=slope2, then the lines are parallel} \\ \text{if slope1}\cdot slope2=-1,\text{ then, the lines are perpendicular} \\ \text{replacing} \\ \text{slope}1\cdot\text{slope}2=\frac{4}{3}\cdot\frac{-11}{4}=\frac{-11}{3} \end{gathered}[/tex]Hence, the lines are not parallel,and the lines are not perpendicular.
I hope this helps you
