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Two points in a plane determine...

Two points in a plane determine

A

exactly one line segment

B

exactly two line segment

C

an infinite number of line segments

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question "Two points in a plane determine," we need to analyze the relationship between two points in a plane and what they can form. ### Step-by-Step Solution: 1. **Understanding Points in a Plane**: - In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. Points are specific locations on this surface. **Hint**: Remember that a plane can contain infinitely many points. 2. **Identifying the Points**: - Let's denote the two points as A and B. These points are distinct and located at different positions in the plane. **Hint**: Think of how you can visualize points on a piece of paper. 3. **Connecting the Points**: - When we connect points A and B with a straight line, we form a line segment. A line segment is defined as the part of a line that is bounded by two distinct endpoints. **Hint**: Recall the definition of a line segment: it has two endpoints. 4. **Determining the Line Segment**: - Since there are only two points, the only line segment we can form is the one that directly connects these two points. There cannot be more than one line segment between two distinct points. **Hint**: Consider how many ways you can connect two points with a straight line. 5. **Conclusion**: - Therefore, two points in a plane determine exactly one line segment. **Hint**: Think about the options provided and how they relate to the concept of a line segment. ### Final Answer: The correct option is **A: exactly one line segment**.
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