Let's solve the problem step-by-step:
1. Understand the given information:
- Points [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are collinear, meaning they lie on a straight line.
- Point [tex]\(B\)[/tex] is between points [tex]\(A\)[/tex] and [tex]\(C\)[/tex].
- The distance [tex]\(AB\)[/tex] is 12 units.
- The distance [tex]\(AC\)[/tex] is 19 units.
2. Recall the geometric relationship on a straight line:
- Since [tex]\(B\)[/tex] is between [tex]\(A\)[/tex] and [tex]\(C\)[/tex], the distance from [tex]\(A\)[/tex] to [tex]\(C\)[/tex] ([tex]\(AC\)[/tex]) can be thought of as the sum of distances [tex]\(AB\)[/tex] and [tex]\(BC\)[/tex].
3. Set up the equation using the given distances:
[tex]\[
AC = AB + BC
\][/tex]
4. Substitute the given values into the equation:
- [tex]\(AC = 19\)[/tex]
- [tex]\(AB = 12\)[/tex]
[tex]\[
19 = 12 + BC
\][/tex]
5. Solve the equation for [tex]\(BC\)[/tex]:
[tex]\[
BC = 19 - 12
\][/tex]
6. Perform the subtraction:
[tex]\[
BC = 7
\][/tex]
So, the distance [tex]\(BC\)[/tex] is [tex]\(7\)[/tex] units.
