Given that points [tex]\( S \)[/tex], [tex]\( U \)[/tex], and [tex]\( N \)[/tex] are collinear, with the distances provided as:
- [tex]\( NU = 1 \)[/tex]
- [tex]\( SU = 2 \)[/tex]
- [tex]\( SN = 3 \)[/tex]
We need to determine which point lies between the other two.
To solve this, we analyze the distances and their sums:
1. Check if [tex]\( U \)[/tex] lies between [tex]\( S \)[/tex] and [tex]\( N \)[/tex]:
- If [tex]\( U \)[/tex] is between [tex]\( S \)[/tex] and [tex]\( N \)[/tex], then the sum of the distances from [tex]\( N \)[/tex] to [tex]\( U \)[/tex] and from [tex]\( S \)[/tex] to [tex]\( U \)[/tex] should equal the distance from [tex]\( S \)[/tex] to [tex]\( N \)[/tex]:
[tex]\[
NU + SU = SN
\][/tex]
Substitute the given distances:
[tex]\[
1 + 2 = 3
\][/tex]
This equation holds true.
Since the sum of [tex]\( NU \)[/tex] and [tex]\( SU \)[/tex] equals [tex]\( SN \)[/tex], it confirms that point [tex]\( U \)[/tex] lies between points [tex]\( S \)[/tex] and [tex]\( N \)[/tex].
Thus, the point [tex]\( U \)[/tex] is between points [tex]\( S \)[/tex] and [tex]\( N \)[/tex].
