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: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line, $y_2=y_1$, so $m = 0$. For a vertical line, $x_2=x_1$, and the slope is undefined.

Step2: Analyze line RS

Line RS is a horizontal line. Let's assume two points on line RS, say $R(x_1,y_1)$ and $S(x_2,y_2)$ where $y_1 = y_2=6$. Then $m_{RS}=\frac{6 - 6}{x_2 - x_1}=0$.

Step3: Analyze line SW

Line SW is a vertical line. Let two points on line SW be $S(x_1,y_1)$ and $W(x_2,y_2)$ with $x_1=x_2 = 2$. Then $m_{SW}=\frac{y_2 - y_1}{2 - 2}$, which is undefined.

Step4: Analyze line TV

Line TV is a horizontal line. Let two points on line TV be $T(x_1,y_1)$ and $V(x_2,y_2)$ with $y_1=y_2=- 4$. Then $m_{TV}=\frac{-4+4}{x_2 - x_1}=0$.

Step5: Check parallel - perpendicular relationships

Horizontal lines are parallel to each other. Since RS and TV are horizontal, they are parallel. A vertical line is perpendicular to a horizontal line. 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.