If a perpendicular is drawn to a line segment MN at N and point P is marked on perpendicular, then

Options

A. `bar(MP) botbar(NP)`
B. `bar(MN) || bar(NP)`
C. `bar(MN)|| bar(MP)`
D. `bar(MN) bot bar(NP)`

Answer

To solve the question step by step, we need to analyze the situation described:

1. **Understanding the Setup**: We have a line segment MN, where N is one of the endpoints. A perpendicular line is drawn at point N, which means it forms a 90-degree angle with the line segment MN. Let's denote the point where the perpendicular line intersects as point P.

**Hint**: Visualize the setup by drawing a line segment MN and marking point N. Then draw a perpendicular line at N.

2. **Identifying the Relationships**: We need to evaluate the relationships between the lines MN, NP, and MP. The options provided in the question suggest different geometric relationships (perpendicularity and parallelism).

**Hint**: Think about the definitions of perpendicular and parallel lines. Perpendicular lines intersect at a right angle, while parallel lines never meet.

3. **Evaluating Each Option**:
- **Option 1**: MP is perpendicular to NP. Since MP is a line segment connecting points M and P, and NP is the perpendicular line from N to P, they do not form a right angle at N. Therefore, this option is incorrect.

**Hint**: Check the angles formed by the lines. Are they 90 degrees?

- **Option 2**: MN is parallel to NP. Since MN and NP intersect at point N, they cannot be parallel. Therefore, this option is also incorrect.

**Hint**: Remember that parallel lines do not meet at any point.

- **Option 3**: MN is parallel to MP. Again, since MP connects M to P and they intersect at N, they cannot be parallel. Thus, this option is incorrect as well.

**Hint**: Look for intersection points to determine if lines are parallel.

- **Option 4**: MN is perpendicular to NP. This is true because NP was specifically drawn as a perpendicular line to MN at point N. Therefore, this option is correct.

**Hint**: Recall that the problem states that the line drawn at N is a perpendicular, confirming this relationship.

4. **Conclusion**: The correct answer is that MN is perpendicular to NP.

**Final Answer**: MN is perpendicular to NP.