To address the question of how many lines can be drawn through any two given points in space, we need to invoke a fundamental principle from Euclidean geometry.
When dealing with points in space, consider the following key ideas:
1. A line in Euclidean geometry is defined as the shortest distance between two points and extends infinitely in both directions through those points.
2. Given two distinct points, there is a unique straight path that connects them. This path is what we term a line.
To break it down step-by-step:
- Let's denote the two distinct points as [tex]\( P_1 \)[/tex] and [tex]\( P_2 \)[/tex].
- Euclidean geometry asserts that through any two distinct points, there exists one and only one straight line.
- This line is uniquely determined by the coordinates of points [tex]\( P_1 \)[/tex] and [tex]\( P_2 \)[/tex]. Because the positions of these points are fixed, the line connecting them is also fixed and unique.
Thus, we can conclude with certainty that the best description for the number of lines that can be drawn through any two given points in space is:
(1) Exactly one line
Therefore, the correct answer is:
```
1) Exactly one line
```
