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. $a(1,5), b(4,4), c(9, - 10), d(-6,-5)$ select choice

Explanation:

Step1: Calculate slope of line AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(1,5)$ and $B(4,4)$, we have $m_{AB}=\frac{4 - 5}{4 - 1}=\frac{-1}{3}=-\frac{1}{3}$.

Step2: Calculate slope of line CD

For points $C(9,-10)$ and $D(-6,-5)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_{CD}=\frac{-5+10}{-6 - 9}=\frac{5}{-15}=-\frac{1}{3}$.

Step3: Determine the relationship

Since $m_{AB}=m_{CD}=-\frac{1}{3}$, the two lines are parallel.

Answer:

Parallel