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In the given problem, points \( A \), \( B \), and \( C \) are collinear, and \( B \) is between \( A \) and \( C \). We are given the following distances:

- \( AB = 12 \)
- \( AC = 19 \)

We need to find the distance \( BC \).

Since \( B \) is between \( A \) and \( C \), the total distance \( AC \) can be expressed as:

\[
AC = AB + BC
\]

Substitute the known values into the equation:

\[
19 = 12 + BC
\]

Now, solve for \( BC \):

\[
BC = 19 - 12 = 7
\]

So, the distance \( BC = 7 \).

Would you like further explanation or details? Here are five related questions for practice:

1. If \( AB = 15 \) and \( AC = 25 \), what is \( BC \)?
2. What happens to \( BC \) if \( B \) is not between \( A \) and \( C \)?
3. If \( AB = 10 \) and \( BC = 5 \), what is the total length of \( AC \)?
4. What mathematical property allows us to add the segments \( AB \) and \( BC \)?
5. How would the equation change if \( C \) were between \( A \) and \( B \)?

**Tip:** Always ensure the points are on the same line and the given segment lengths add up logically when solving for unknown distances in collinear point problems.

Points A, B, and C are collinear, and B is between A and C. Given AB = 12 and AC = 19, what is BC?

Learn how to solve for BC in a collinear points problem where AB = 12 and AC = 19. This problem focuses on geometry concepts like segment addition and collinearity, suitable for students in Grades 6-8.

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