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:

Identify coordinates and equations of the lines

Using the Slope of a Line knowledge point, we first determine the coordinates of the points defining each line from the graph:

• Line \(RS\) passes through \(R(-8, 6)\) and \(S(2, 6)\). Since the \(y\)-coordinates are equal, this is a horizontal line with the equation \(y = 6\).
• Line \(TV\) passes through \(T(-5, -4)\) and \(V(8, -4)\). Since the \(y\)-coordinates are equal, this is a horizontal line with the equation \(y = -4\).
• Line \(SW\) passes through \(S(2, 6)\) and \(W(2, -8)\). Since the \(x\)-coordinates are equal, this is a vertical line with the equation \(x = 2\).

Analyze the slopes of the lines

Using the Slope of a Line knowledge point

• The slope of a horizontal line is \(0\). Thus, the slope of line \(RS\) is \(0\), and the slope of line \(TV\) is \(0\).
• The slope of a vertical line is undefined. Thus, the slope of line \(SW\) is undefined.

Analyze parallel relationships

Using the Parallel Line Equations knowledge point

• Two non-vertical lines are parallel if and only if they have the same slope.
• Since both line \(RS\) and line \(TV\) are horizontal lines with a slope of \(0\), they are parallel to each other.

Analyze perpendicular relationships

Using the Perpendicular Line Equations knowledge point

• A horizontal line and a vertical line are always perpendicular to each other.
• Since line \(SW\) is vertical, and both lines \(RS\) and \(TV\) are horizontal, line \(SW\) is perpendicular to both line \(RS\) and line \(TV\).

Evaluate the given options

We compare our findings to the five statements:

1. "Line RS has a slope of 6." (False, its slope is \(0\).)
2. "Line SW has an undefined slope." (True, since it is a vertical line.)
3. "Line TV has a slope of 0." (True, since it is a horizontal line.)
4. "Lines RS and TV are parallel." (True, since both are horizontal lines.)
5. "Line SW is perpendicular to line RS, but not to line TV." (False, it is perpendicular to both.)

Answer:

• Line RS has a slope of 6.
• Line SW has an undefined slope. (Correct answer)
• Line TV has a slope of 0. (Correct answer)
• Lines RS and TV are parallel. (Correct answer)
• Line SW is perpendicular to line RS, but not to line TV.