On a number​ line, the coordinates of​ X, Y,​ Z, and W are negative 6​, negative 4​, 3​, and 7​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent.

To find the lengths of the segments \( XY \) and \( ZW \), we use the formula for the distance between two points on a number line:

\[
\text{Distance} = | x_2 - x_1 |
\]

### Step 1: Find the length of segment \( XY \)
The coordinates of \( X \) and \( Y \) are \( -6 \) and \( -4 \), respectively. The length of segment \( XY \) is:
\[
XY = | -4 - (-6) | = | -4 + 6 | = | 2 | = 2
\]

### Step 2: Find the length of segment \( ZW \)
The coordinates of \( Z \) and \( W \) are \( 3 \) and \( 7 \), respectively. The length of segment \( ZW \) is:
\[
ZW = | 7 - 3 | = | 4 | = 4
\]

### Step 3: Compare the lengths
The length of segment \( XY \) is \( 2 \), and the length of segment \( ZW \) is \( 4 \).

Since \( 2 \neq 4 \), the two segments are **not congruent**.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How do we determine the distance between two points on a number line in general?
2. Can the absolute value formula be used for all types of number line problems?
3. What are some properties of congruent segments?
4. How would the process change if the points were in two dimensions instead of one?
5. Can two segments with different lengths ever be congruent under any conditions?

**Tip:** Always use absolute value when calculating distances, as distances are non-negative.

On a number line, the coordinates of X, Y, Z, and W are negative 6, negative 4, 3, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent.

Learn how to find the lengths of two segments on a number line with coordinates X = -6, Y = -4, Z = 3, and W = 7. This solution uses the distance formula and explores whether the segments are congruent. Suitable for Grades 6-8.

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