Question

is $overrightarrow{ab}$ parallel to $overrightarrow{cd}$? explain. yes, because both lines have a slope of $\frac{4}{3}$. yes, because both lines have a slope of $\frac{3}{4}$. no, because the slopes of the lines are not equal. no, because the slopes of the lines are not opposite reciprocals of each other. a(-3,-3) b(0,1) c(0,-5) d(3,-1)

Explanation:

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

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-3,-3)$ and $B(0,1)$, we have $x_1=-3,y_1 = - 3,x_2=0,y_2 = 1$. Then $m_{AB}=\frac{1-(-3)}{0 - (-3)}=\frac{4}{3}$.

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

For points $C(0,-5)$ and $D(3,-1)$, we have $x_1 = 0,y_1=-5,x_2=3,y_2=-1$. Then $m_{CD}=\frac{-1-(-5)}{3 - 0}=\frac{4}{3}$.

Step3: Determine parallel - ness

Two non - vertical lines are parallel if and only if their slopes are equal. Since $m_{AB}=m_{CD}=\frac{4}{3}$, $\overrightarrow{AB}$ is parallel to $\overrightarrow{CD}$.

Answer:

Yes, because both lines have a slope of $\frac{4}{3}$.