To solve the problem, we are tasked with finding the length of segment $AB$. The length is calculated as the absolute value of the difference between the two endpoints:

$AB = |B - A|$

Here, $A = 13$ and $B = 34$. Substituting these values:

$AB = |34 - 13| = |21| = 21$

Thus, the length of $AB$ is $21$.

Would you like further clarification or detailed steps?

Here are five related questions for further exploration:

1. What would the length of $AB$ be if $A = 5$ and $B = 25$?
2. How do you find the length of a segment on a number line with negative coordinates?
3. Can you explain why the absolute value is necessary in measuring segment lengths?
4. How do you calculate the midpoint of segment $AB$?
5. What is the difference between distance and displacement?

Tip: Always check for negative coordinates when finding distances to ensure correct use of the absolute value.