High School

Point [tex] M [/tex] is between points [tex] N [/tex] and [tex] O [/tex] on [tex] \overline{N O} [/tex].

Find the length of [tex] \overline{N M} [/tex] if [tex] M O = 12.3 [/tex] and [tex] N O = 26.9 [/tex].

A. 11.6
B. 14.6
C. 21.6
D. 38.2

Please select the best answer from the choices provided:
A
B
C
D

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].