Question

check for understanding
determine whether $overrightarrow{ab}$ and $overrightarrow{cd}$ are
parallel, perpendicular, or neither
for $a(14,13), b(-11,0), c(-3,7),$
and $d(-4,-5)$. graph each line
to verify your answer.

Explanation:

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

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(14,13)$ and $B(-11,0)$, we have $m_{AB}=\frac{0 - 13}{-11 - 14}=\frac{-13}{-25}=\frac{13}{25}$.

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

For points $C(-3,7)$ and $D(-4,-5)$, we have $m_{CD}=\frac{-5 - 7}{-4+3}=\frac{-12}{-1}=12$.

Step3: Check relationship

Two lines are parallel if their slopes are equal ($m_{AB}=m_{CD}$), perpendicular if the product of their slopes is - 1 ($m_{AB}\times m_{CD}=-1$). Since $\frac{13}{25}
eq12$ and $\frac{13}{25}\times12=\frac{156}{25}
eq - 1$, the lines are neither parallel nor perpendicular.

Answer:

Neither