https://file.aiquickdraw.com/mathbot/file/1727936344617aqyatnnx.jpg

Let's break down and solve the problem step by step.

### Given Information:
- Coordinates of \( X = -7 \)
- Coordinates of \( Y = -3 \)
- Coordinates of \( Z = 4 \)
- Coordinates of \( W = 10 \)

### Required:
- Find the lengths of line segments \( \overline{XY} \) and \( \overline{ZW} \).
- Determine if these segments are congruent (i.e., have equal lengths).

### Step 1: Find the Length of \( \overline{XY} \)
The length of a line segment between two points on a number line is simply the absolute difference between their coordinates. So,

\[
\text{Length of } \overline{XY} = |X - Y| = |-7 - (-3)| = |-7 + 3| = |-4| = 4
\]

### Step 2: Find the Length of \( \overline{ZW} \)
Similarly, for \( \overline{ZW} \),

\[
\text{Length of } \overline{ZW} = |Z - W| = |4 - 10| = |-6| = 6
\]

### Step 3: Compare the Two Segments
- The length of \( \overline{XY} \) is 4.
- The length of \( \overline{ZW} \) is 6.

Since \( 4 \neq 6 \), the two segments \( \overline{XY} \) and \( \overline{ZW} \) are **not congruent**.

---

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions you can explore:
1. How do you find the midpoint of a segment on a number line?
2. What is the formula for the distance between two points in a coordinate plane?
3. What are congruent segments, and what are some examples in geometry?
4. How would you find the length of a segment if it involved coordinates in 2D space?
5. Can two segments have different coordinates and still be congruent?

**Tip:** The absolute value ensures that the length of a segment is always positive, no matter the direction on the number line.

On a number line, the coordinates of X, Y, Z, and W are −7, −3, 4, and 10, respectively. Find the lengths of the two segments XY and ZW. Then tell whether they are congruent.

Learn how to find the lengths of segments XY and ZW on a number line, given the coordinates of points X(-7), Y(-3), Z(4), and W(10). The solution involves calculating the distance between two points and determining whether the segments are congruent. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation