Question

select whether $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ are parallel, perpendicular, or neither. graph each line on a separate sheet of paper to verify your answer. a(8, -2), b(4, -1), c(3, 11), d(-2, -9)
select choice

Explanation:

Step1: Calculate slope of $\overleftrightarrow{AB}$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(8,-2)$ and $B(4,-1)$, $m_{AB}=\frac{-1-(-2)}{4 - 8}=\frac{-1 + 2}{-4}=-\frac{1}{4}$.

Step2: Calculate slope of $\overleftrightarrow{CD}$

For points $C(3,11)$ and $D(-2,-9)$, $m_{CD}=\frac{-9 - 11}{-2-3}=\frac{-20}{-5}=4$.

Step3: Analyze the relationship

Two lines are parallel if their slopes are equal. Two lines are perpendicular if the product of their slopes is - 1. Since $m_{AB}\times m_{CD}=-\frac{1}{4}\times4=-1$, the lines are perpendicular.

Answer:

Perpendicular