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.

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.