https://file.aiquickdraw.com/mathbot/file/1727925917160qfs2i1n3.jpg

Let's go through the problem step by step.

The coordinates of points \( X \), \( Y \), \( Z \), and \( W \) are given as:
- \( X = -8 \)
- \( Y = -5 \)
- \( Z = 2 \)
- \( W = 5 \)

### 1. Find the length of segment \( XY \):
To find the length of a segment on a number line, subtract the smaller coordinate from the larger coordinate.

\[
\text{Length of } XY = |X - Y| = |-8 - (-5)| = |-8 + 5| = | -3 | = 3
\]

### 2. Find the length of segment \( ZW \):
Similarly, for segment \( ZW \):

\[
\text{Length of } ZW = |Z - W| = |2 - 5| = |-3| = 3
\]

### 3. Determine if the segments are congruent:
Since both segments \( XY \) and \( ZW \) have the same length (3 units), they are congruent.

Thus, the answers are:
- The length of \( XY \) is **3**.
- The length of \( ZW \) is **3**.
- Are the segments congruent? **Yes**.

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Would you like further details or have any questions? 

Here are 5 related questions for more practice:
1. If \( A = -10 \) and \( B = -2 \), what is the length of segment \( AB \)?
2. What is the distance between points \( X = 3 \) and \( Y = -4 \) on a number line?
3. Can two segments with different coordinates ever be congruent? Why?
4. If segment \( XY \) is 4 units long, and \( X = 7 \), what is the possible value of \( Y \)?
5. What does it mean for two segments to be congruent geometrically?

**Tip**: On a number line, the distance between two points is always the absolute value of their difference, regardless of direction.

On a number line, the coordinates of X, Y, Z, and W are -8, -5, 2, and 5, respectively. Find the lengths of the two segments XY and ZW. Then tell whether they are congruent.

Solve the problem of finding the lengths of two segments on a number line where X = -8, Y = -5, Z = 2, and W = 5. Learn how to calculate distances and determine if the segments are congruent. Suitable for students in Grades 6-8.

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