https://file.aiquickdraw.com/mathbot/file/1727105111620488b7ie5.jpg

The problem describes two points, \( Y \) and \( Z \), on a number line. You are given the following information:

1. The distance between \( Y \) and \( Z \), denoted by \( YZ \), is 10 units.
2. \( Y \) is located at 13.

You need to determine the possible locations of \( Z \).

### Solution:
- Since the distance between \( Y \) and \( Z \) is 10 units, \( Z \) can be located either:
  - 10 units to the right of \( Y \), or
  - 10 units to the left of \( Y \).

To calculate the possible locations of \( Z \):
1. \( Z \) could be at \( Y + 10 \), which is \( 13 + 10 = 23 \).
2. \( Z \) could also be at \( Y - 10 \), which is \( 13 - 10 = 3 \).

### Conclusion:
The two possible locations of \( Z \) are \( 3 \) and \( 23 \).

### Final Answer:
Locations of \( Z \): \( 3, 23 \)

---

Would you like further details on this?  
Here are 5 additional related questions to explore:
1. What if \( YZ = 15 \) instead of 10? Where could \( Z \) be?
2. How would you represent this problem geometrically on a number line?
3. Can you generalize a formula for the location of \( Z \) given any point \( Y \) and distance \( d \)?
4. What happens if the distance \( YZ \) is negative?
5. How can this concept apply to real-world measurements or physics?

**Tip:** When working with distances on a number line, always remember that there are two directions—positive (to the right) and negative (to the left).

Suppose that Y and Z are points on the number line. If YZ = 10 and Y lies at 13, where could Z be located?

This problem involves finding the location(s) of point Z on a number line, given that the distance between points Y and Z is 10 units and Y is located at 13. Learn how to apply the distance formula for points on a number line. Suitable for students in 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