To check if those segments are parallel, we can compare the slope of the lines that contain them. To find the slope using two points, we can use the following formula
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Using this formula for the segment AB, we have
[tex]m_1=\frac{((-2)-3)}{((-12)-(-8))_{}}=\frac{-5}{-12+8}=\frac{5}{4}[/tex]
Now, using this formula for CD
[tex]m_2_{}=\frac{((-7)-(-3))}{((-2)-(-7))_{}}=\frac{-7+3}{-2+7}=-\frac{4}{5}[/tex]
When the slopes are equal, the lines are parallel, if one slope is minus the inverse of the other, they are perpendicular, otherwise they are neither.
Since
[tex]\frac{5}{4}=-(-\frac{4}{5})^{-1}\Rightarrow m_1=-\frac{1}{m_2}[/tex]
They are perpendicular.
