Understanding the Concept of a Line
To comprehend why 2 points are sufficient to determine a line, let's break down the concept of a line in geometry.
Definition of a Line
- A line is a straight one-dimensional figure that extends infinitely in both directions.
- It is defined by its direction and position in space.
Why 2 Points are Sufficient
- Two Points Determine a Line:
- Any two distinct points in a plane can always be connected by a straight line.
- No matter where these points are located, you can always draw a single straight line that passes through both.
- Collinearity of Points:
- If you have more than two points, they may or may not lie on the same line (collinear).
- Therefore, while you can define a line with two points, adding a third point could either confirm they are collinear or indicate they do not lie on the same line.
Examples of Points Determining a Line
- Example 1:
- Points A (1, 2) and B (3, 4) can define a line uniquely.
- Example 2:
- If you have points C (2, 3) and D (5, 7), you can again draw a line through these two points.
Conclusion
- In summary, the correct answer is option 'A': 2 points are enough to fix a line.
- This principle is foundational in geometry, illustrating the simplicity and clarity of linear relationships.