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 Perpendicular/Parallel Lines

If a line is perpendicular to two other lines, those two lines are parallel (since they both have the same relationship with the perpendicular line, meaning their slopes are equal, so they are parallel).

Step2: Analyze Each Option

• Option 1: Line TU is parallel to line RS. Since WV is perpendicular to both, RS and TU must be parallel (same slope, as both are perpendicular to WV).
• Option 2: TU can't be perpendicular to RS (they are parallel, not perpendicular).
• Option 3: TU has a slope (it's not vertical), so "no slope" is wrong.
• Option 4: Slope of TU isn't -5 (from graph, it's a shallow slope, not -5).

Answer:

Line TU is parallel to line RS.