Point M is the midpoint of Line Segment AB. Point N is the midpoint of Line Segment AM. If AN = 7 , then what is the length of Line Segment AB ?

We are given that:

- Point \( M \) is the midpoint of line segment \( AB \),
- Point \( N \) is the midpoint of line segment \( AM \),
- The length of segment \( AN = 7 \).

### Step-by-step solution:

1. Let the total length of line segment \( AB \) be \( L \).
   
2. Since \( M \) is the midpoint of \( AB \), the length of segment \( AM \) is half of \( AB \):
   \[
   AM = \frac{L}{2}
   \]

3. Point \( N \) is the midpoint of \( AM \), so the length of segment \( AN \) is half of \( AM \):
   \[
   AN = \frac{AM}{2} = \frac{\frac{L}{2}}{2} = \frac{L}{4}
   \]

4. We are told that \( AN = 7 \), so:
   \[
   \frac{L}{4} = 7
   \]

5. Solving for \( L \):
   \[
   L = 7 \times 4 = 28
   \]

### Conclusion:
The length of line segment \( AB \) is \( \boxed{28} \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the formula to find the midpoint of a line segment on a coordinate plane?
2. How do you find the length of a line segment given its endpoints in a coordinate plane?
3. If the midpoint is given, how do you find the endpoints of a segment?
4. How can you divide a line segment into any ratio?
5. What are some real-world applications of midpoints?

**Tip**: Midpoints divide a line segment into two equal parts, which is crucial for geometric constructions and problem-solving.

Point M is the midpoint of Line Segment AB. Point N is the midpoint of Line Segment AM. If AN = 7, then what is the length of Line Segment AB?

Learn how to find the length of Line Segment AB using the Midpoint Theorem. The problem involves basic geometry concepts such as midpoints and line segments. This solution is suitable for students in Grades 6-8.

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