https://file.aiquickdraw.com/mathbot/file/1727236860041tuzxsy8e.jpg

To solve this problem, let's find the lengths of the segments \(\overline{XY}\) and \(\overline{ZW}\) using the given coordinates on the number line.

### Coordinates:
- \( X = -7 \)
- \( Y = -5 \)
- \( Z = 4 \)
- \( W = 8 \)

### Calculating the lengths:

1. **Length of \(\overline{XY}\):**
   \[
   \text{Length of } \overline{XY} = |Y - X| = |-5 - (-7)| = |-5 + 7| = |2| = 2
   \]

2. **Length of \(\overline{ZW}\):**
   \[
   \text{Length of } \overline{ZW} = |W - Z| = |8 - 4| = |4| = 4
   \]

### Conclusion:
- The length of \(\overline{XY}\) is 2.
- The length of \(\overline{ZW}\) is 4.

Since the lengths are different, the segments \(\overline{XY}\) and \(\overline{ZW}\) are **not congruent**.

Would you like more details or have any questions?

### Related Questions:
1. How do you find the length of a segment between two points on a coordinate plane?
2. What does it mean for two segments to be congruent?
3. How can you determine the midpoint of a segment on a number line?
4. How do absolute values affect calculations involving distance?
5. Can two segments be congruent if their lengths are decimals or fractions?

### Tip:
When finding the length of a segment on a number line, always use the absolute value of the difference between the two coordinates to ensure the result is positive.

On a number line, the coordinates of X, Y, Z, and W are −7, −5, 4, and 8, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and ZW.

Discover how to calculate the lengths of segments XY and ZW on a number line, using coordinates -7, -5, 4, and 8. The problem focuses on coordinate geometry and congruence, suitable for Grades 6-8.

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