Let's break down this scenario step-by-step:
1. Understanding the Line Segment:
- We are given three points: [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]. The point [tex]\( A \)[/tex] is between [tex]\( B \)[/tex] and [tex]\( C \)[/tex], which means they lie on a straight line in that order: [tex]\( B \)[/tex], [tex]\( A \)[/tex], [tex]\( C \)[/tex].
2. Positions and Distances:
- Let's denote the distance between points [tex]\( B \)[/tex] and [tex]\( A \)[/tex] as [tex]\( BA \)[/tex].
- Similarly, denote the distance between points [tex]\( A \)[/tex] and [tex]\( C \)[/tex] as [tex]\( AC \)[/tex].
- The distance between the points [tex]\( B \)[/tex] and [tex]\( C \)[/tex] is denoted as [tex]\( BC \)[/tex].
3. Combining the Segments:
- Since point [tex]\( A \)[/tex] lies between points [tex]\( B \)[/tex] and [tex]\( C \)[/tex], the total distance from [tex]\( B \)[/tex] to [tex]\( C \)[/tex] is the sum of the distances [tex]\( BA \)[/tex] and [tex]\( AC \)[/tex].
- Mathematically, we write this relationship as:
[tex]\[
BA + AC = BC
\][/tex]
4. Verification with Example Values:
- Let [tex]\( BA = 3 \)[/tex] units.
- Let [tex]\( AC = 5 \)[/tex] units.
- Then, the total distance [tex]\( BC \)[/tex] is:
[tex]\[
BC = BA + AC = 3 + 5 = 8 \text{ units}
\][/tex]
5. Conclusion:
- We verified with the example values that [tex]\( BA + AC \)[/tex] indeed equals [tex]\( BC \)[/tex]. This confirms the relationship holds true.
Given this reasoning and verification with numeric example, the correct answer to the statement "If point [tex]\( A \)[/tex] is between [tex]\( B \)[/tex] and [tex]\( C \)[/tex], then [tex]\( BA + AC = BC \)[/tex]" is always true.
