https://r2.erweima.ai/mathbot/image/17238582855299u52411d.jpg

Find the length of the of YZ if XZ is 10,WZ is 14, and WY is 11

To find the length of \( YZ \) given the lengths of \( XZ \), \( WZ \), and \( WY \), we can use the relationships between the points on the number line. Let's assign the coordinates of the points as follows:

- Let \( W \) be at \( w \)
- Let \( X \) be at \( x \)
- Let \( Y \) be at \( y \)
- Let \( Z \) be at \( z \)

From the problem, we know:
- \( XZ = z - x = 10 \)
- \( WZ = z - w = 14 \)
- \( WY = y - w = 11 \)

We are required to find \( YZ = z - y \).

### Step 1: Express \( x \), \( y \), and \( z \) in terms of \( w \)
1. \( z = w + 14 \) (from \( WZ = 14 \))
2. \( x = z - 10 = w + 14 - 10 = w + 4 \) (from \( XZ = 10 \))
3. \( y = w + 11 \) (from \( WY = 11 \))

### Step 2: Find \( YZ \)
\[ YZ = z - y = (w + 14) - (w + 11) = 14 - 11 = 3 \]

So, the length of \( YZ \) is \( 3 \) units.

Would you like further details or have any questions?

---

**Related Questions:**
1. How would the solution change if \( WX \) were given instead of \( WY \)?
2. If \( WZ \) were given as \( 16 \) instead of \( 14 \), what would \( YZ \) be?
3. How does this problem relate to the concept of segment addition?
4. What if \( Y \) was between \( X \) and \( Z \)? How would that affect the calculation of \( YZ \)?
5. Can you prove the result using the midpoint theorem?
6. What if \( XW \) was given instead of \( WZ \)? How would you approach the problem?
7. How does this solution extend to three-dimensional coordinates?
8. If \( WY \) was given as \( 15 \), how would that affect the result?

**Tip:** Always double-check the coordinates you assign to each point on a number line to avoid mistakes in calculations!

Learn how to find the length of YZ using coordinate geometry. Given XZ = 10, WZ = 14, and WY = 11, understand the relationships between points and calculate YZ step-by-step. Suitable for high school students studying coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation