Question

is (overrightarrow{tu}) parallel to (overrightarrow{vw})? explain. no, because both lines have a slope of (\frac{3}{2}) no, because the slopes of the lines are not equal yes, because both lines have a slope of (\frac{2}{3}) yes, because the slopes of the lines are not equal t(-6,1) u(9,11) v(3, -7) w(9, -3)

Explanation:

Step1: Calculate slope of line $\overrightarrow{TU}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $T(-6,1)$ and $U(9,11)$, we have $m_{TU}=\frac{11 - 1}{9-(-6)}=\frac{10}{15}=\frac{2}{3}$.

Step2: Calculate slope of line $\overrightarrow{VW}$

For points $V(3,-7)$ and $W(9,-3)$, we have $m_{VW}=\frac{-3-(-7)}{9 - 3}=\frac{4}{6}=\frac{2}{3}$.

Step3: Determine parallel - ness

Two non - vertical lines are parallel if and only if their slopes are equal. Since $m_{TU}=m_{VW}=\frac{2}{3}$, $\overrightarrow{TU}$ is parallel to $\overrightarrow{VW}$.

Answer:

yes, because both lines have a slope of $\frac{2}{3}$