https://file.aiquickdraw.com/mathbot/file/1727452551574ywg1t1jz.png

To solve the problem, we are given the coordinates of points X, Y, Z, and W on a number line:

- \( X = -8 \)
- \( Y = -6 \)
- \( Z = 3 \)
- \( W = 5 \)

We are tasked with finding the length of the segment \( XZ \). 

The length of a segment on a number line is the absolute difference between the coordinates of the two points. In this case, we need to find the distance between \( X = -8 \) and \( Z = 3 \). 

The formula for the distance between two points on a number line is:

\[
\text{Distance} = |Z - X|
\]

Substituting the values:

\[
\text{Distance} = |3 - (-8)| = |3 + 8| = |11| = 11
\]

Thus, the length of segment \( XZ \) is 11 units.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the distance between two points in a coordinate plane (not just on a number line)?
2. What is the length of segment \( YW \) given the same coordinates?
3. Can the distance between two points ever be negative? Why or why not?
4. How would you calculate the midpoint of segment \( XZ \)?
5. How does the distance formula change when dealing with three-dimensional coordinates?

**Tip:** When working with number lines or coordinate geometry, always take the absolute value to ensure distances remain non-negative.

On a number line, the coordinates of X, Y, Z, and W are -8, -6, 3, and 5, respectively. Find the lengths of the segment XZ.

Solve the problem of finding the length of segment XZ on a number line with coordinates X = -8 and Z = 3. Learn how to apply the distance formula |Z - X| to find the distance between points. Suitable for students in Grades 6-8.

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