Question

lines rs, tv, and sw are shown.
which statements are true about these lines? select three options.
□ line rs has a slope of 6.
□ line sw has an undefined slope.
□ line tv has a slope of 0.
□ lines rs and tv are parallel.
□ line sw is perpendicular to line rs, but not to line tv.

Explanation:

Step1: Find slope of line RS

Line RS is horizontal, passing through $y=6$. Slope formula: $\text{slope} = \frac{y_2-y_1}{x_2-x_1}$. For $R(-8,6)$ and $S(2,6)$:
$\text{slope}_{RS} = \frac{6-6}{2-(-8)} = \frac{0}{10} = 0$

Step2: Find slope of line SW

Line SW is vertical, passing through $x=2$. For $S(2,6)$ and $W(2,-8)$:
$\text{slope}_{SW} = \frac{-8-6}{2-2} = \frac{-14}{0}$, which is undefined.

Step3: Find slope of line TV

Line TV is horizontal, passing through $y=-4$. For $T(-6,-4)$ and $V(8,-4)$:
$\text{slope}_{TV} = \frac{-4-(-4)}{8-(-6)} = \frac{0}{14} = 0$

Step4: Check parallel/perpendicular

Horizontal lines (slope 0) are parallel, so RS || TV. Vertical lines (undefined slope) are perpendicular to horizontal lines, so SW is perpendicular to both RS and TV.

Answer:

• Line SW has an undefined slope.
• Line TV has a slope of 0.
• Lines RS and TV are parallel.