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: Calculate the slope of line RS

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line RS, assume \(R(- 8,6)\) and \(S(2,6)\). Then \(m_{RS}=\frac{6 - 6}{2-(-8)}=\frac{0}{10}=0\).

Step2: Analyze the slope of line SW

Line SW is a vertical line. The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a vertical line \(x_2=x_1\), so the denominator is \(0\). A slope with a denominator of \(0\) is undefined.

Step3: Calculate the slope of line TV

Assume \(T(-6,-4)\) and \(V(10,-4)\). Then \(m_{TV}=\frac{-4-(-4)}{10 - (-6)}=\frac{0}{16}=0\).

Step4: Check parallelism

Two lines are parallel if they have the same slope. Since \(m_{RS}=0\) and \(m_{TV}=0\), lines RS and TV are parallel.

Step5: Check perpendicularity

A horizontal line (slope \(m = 0\)) and a vertical line (undefined slope) are perpendicular. Since line RS is horizontal and line SW is vertical, line SW is perpendicular to line RS. Also, since line TV is horizontal (slope \(m = 0\)) and line SW is vertical (undefined slope), line SW is perpendicular to line TV.

Answer:

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