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The image shows a problem asking to find the distances between points \(P\), \(Q\), and \(R\) on a number line. The coordinates are:

- \(P = -137\)
- \(Q = -52\)
- \(R = 91\)

### To find \(PQ\) and \(QR\):

1. **Distance \(PQ\)**:
   \[
   PQ = |Q - P| = |-52 - (-137)| = |-52 + 137| = |85| = 85
   \]

2. **Distance \(QR\)**:
   \[
   QR = |R - Q| = |91 - (-52)| = |91 + 52| = |143| = 143
   \]

### Final Answer:
- \(PQ = 85\)
- \(QR = 143\)

Would you like more details or have any other questions?

Here are five related questions you might find useful:
1. How do you find the total distance from \(P\) to \(R\)?
2. Can the distance between two points ever be negative?
3. How would the distances change if \(P\), \(Q\), and \(R\) were in 3D space?
4. What would happen if one of the points were at zero?
5. How can you verify the distances using a number line?

**Tip**: When working with absolute values in distance problems, always subtract in the correct order and take the absolute value to ensure the distance is positive.

Find each distance or angle measure for points P = -137, Q = -52, and R = 91. Calculate PQ and QR.

Learn how to find the distance between points P = -137, Q = -52, and R = 91 on a number line using the absolute value formula. This step-by-step solution covers distances PQ and QR, perfect for students in Grades 6-8.

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