The image shows a geometry problem involving the segment addition axiom. The given diagram shows a line segment with points $A$, $B$, and $C$, where:

• $AB = ?$ (unknown)
• $BC = 10$
• $AC = 12$

To find the length of segment $AB$, we can use the segment addition axiom, which states:

$AB + BC = AC$

Substituting the known values:

$AB + 10 = 12$

Solving for $AB$:

$AB = 12 - 10 = 2$

Thus, the length of segment $AB$ is 2 units.

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

1. What is the segment addition axiom in geometry?
2. How would the solution change if $BC$ were longer than $AC$?
3. What happens if the total segment length $AC$ is not greater than $BC$?
4. Can you apply the segment addition axiom in three-dimensional geometry?
5. How can you use the segment addition axiom to solve problems involving multiple points on a line?

Tip: Always double-check given values and their relationships when using geometric axioms to ensure accurate solutions.