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.