Answer :
To solve this problem, we need to find the length of segment [tex]\(\overline{N M}\)[/tex] given that point [tex]\(M\)[/tex] is between points [tex]\(N\)[/tex] and [tex]\(O\)[/tex] on the line segment [tex]\(\overline{N O}\)[/tex].
We are given:
- The length of [tex]\(\overline{M O} = 12.3\)[/tex].
- The total length of [tex]\(\overline{N O} = 26.9\)[/tex].
Since point [tex]\(M\)[/tex] is between [tex]\(N\)[/tex] and [tex]\(O\)[/tex], we can use the segment addition property, which states that the sum of the lengths of [tex]\(\overline{N M}\)[/tex] and [tex]\(\overline{M O}\)[/tex] is equal to the length of [tex]\(\overline{N O}\)[/tex].
In equation form:
[tex]\[
NM + MO = NO
\][/tex]
We need to solve for [tex]\(NM\)[/tex]. Rearrange the equation to find [tex]\(NM\)[/tex]:
[tex]\[
NM = NO - MO
\][/tex]
Substitute the given values:
[tex]\[
NM = 26.9 - 12.3
\][/tex]
Doing the subtraction:
[tex]\[
NM = 14.6
\][/tex]
Therefore, the length of [tex]\(\overline{N M}\)[/tex] is [tex]\(14.6\)[/tex].
The correct answer is [tex]\(B\)[/tex].
We are given:
- The length of [tex]\(\overline{M O} = 12.3\)[/tex].
- The total length of [tex]\(\overline{N O} = 26.9\)[/tex].
Since point [tex]\(M\)[/tex] is between [tex]\(N\)[/tex] and [tex]\(O\)[/tex], we can use the segment addition property, which states that the sum of the lengths of [tex]\(\overline{N M}\)[/tex] and [tex]\(\overline{M O}\)[/tex] is equal to the length of [tex]\(\overline{N O}\)[/tex].
In equation form:
[tex]\[
NM + MO = NO
\][/tex]
We need to solve for [tex]\(NM\)[/tex]. Rearrange the equation to find [tex]\(NM\)[/tex]:
[tex]\[
NM = NO - MO
\][/tex]
Substitute the given values:
[tex]\[
NM = 26.9 - 12.3
\][/tex]
Doing the subtraction:
[tex]\[
NM = 14.6
\][/tex]
Therefore, the length of [tex]\(\overline{N M}\)[/tex] is [tex]\(14.6\)[/tex].
The correct answer is [tex]\(B\)[/tex].
