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[tex]$S, U, N$[/tex] are collinear. What point is between the other two if [tex]$NU=1$[/tex], [tex]$SU=2$[/tex], [tex]$SN=3$[/tex]?

A. [tex]$S$[/tex]
B. [tex]$U$[/tex]
C. [tex]$N$[/tex]

Sagot :

GinnyAnsweridn
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].
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