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.

Answer :

Sure! Let's solve this step by step.

We are given:
- The length of [tex]\( \overline{MO} \)[/tex] is 12.3 units.
- The length of [tex]\( \overline{NO} \)[/tex] is 26.9 units.

We need to find the length of [tex]\( \overline{NM} \)[/tex].

1. Since point [tex]\( M \)[/tex] is between points [tex]\( N \)[/tex] and [tex]\( O \)[/tex] on [tex]\( \overline{NO} \)[/tex], the segments [tex]\( \overline{NM} \)[/tex] and [tex]\( \overline{MO} \)[/tex] add up to the entire length of [tex]\( \overline{NO} \)[/tex].

2. We can write this relationship as:
[tex]\[
NM + MO = NO
\][/tex]

3. Rearrange the equation to solve for [tex]\( \overline{NM} \)[/tex]:
[tex]\[
NM = NO - MO
\][/tex]

4. Substitute the given values:
[tex]\[
NM = 26.9 - 12.3
\][/tex]

5. Perform the subtraction:
[tex]\[
NM = 14.6
\][/tex]

So, the length of [tex]\( \overline{NM} \)[/tex] is 14.6 units.

Therefore, the correct answer is:
B. 14.6

Other Questions