Question

line wv is perpendicular to both line rs and line tu. which statement must be true about line tu? line tu is parallel to line rs. line tu is perpendicular to line rs. line tu has no slope. line tu has a slope of –5.

Explanation:

Step1: Recall the theorem about perpendicular lines

If a line is perpendicular to two other lines, then those two lines are parallel to each other. This is based on the property of parallel lines and transversals in geometry (specifically, the property related to perpendicular transversals: if two lines are perpendicular to the same line, they are parallel).

Step2: Analyze the given information

We know that line WV is perpendicular to both line RS and line TU. By the theorem from Step 1, line RS and line TU must be parallel to each other.

Step3: Evaluate the other options

• "Line TU is perpendicular to line RS": This is false because we just concluded they are parallel (from the theorem, if two lines are perpendicular to the same line, they can't be perpendicular to each other unless they are the same line, which they aren't here).
• "Line TU has no slope": A line with no slope is a vertical line. From the graph, line TU is not vertical (it's a red line with a non - vertical, non - undefined slope), so this is false.
• "Line TU has a slope of - 5": From the graph, we can see that the slope of line TU is not - 5 (it's a shallow - sloped line), so this is false.

Answer:

Line TU is parallel to line RS.