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.