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.