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To solve for \( FE \) and \( DE \), we need to calculate the distances between the points \( F \), \( E \), and \( D \) on the number line using their respective coordinates.

Given:
- \( D = -10.2 \)
- \( E = -5 \)
- \( F = 12.9 \)

### Step 1: Find \( FE \) (the distance between points \( F \) and \( E \))
The distance between two points on a number line is the absolute difference between their coordinates:
\[
FE = |F - E| = |12.9 - (-5)| = |12.9 + 5| = |17.9| = 17.9
\]

### Step 2: Find \( DE \) (the distance between points \( D \) and \( E \))
\[
DE = |D - E| = |-10.2 - (-5)| = |-10.2 + 5| = |-5.2| = 5.2
\]

Thus:
\[
FE = 17.9, \quad DE = 5.2
\]

Would you like a further explanation of how distances on a number line are calculated?

### Related Questions:
1. How do we calculate distances between points in a coordinate plane instead of a number line?
2. What is the formula for the distance between two points in 3D space?
3. How do we interpret negative coordinates in a number line problem?
4. Can this method be applied to any kind of number (fractions, decimals)?
5. What are some common mistakes when finding distances on a number line?

**Tip**: Always subtract smaller values from larger ones when finding distances to avoid confusion with negative signs.

Find FE and DE based on points F = 12.9, E = -5, and D = -10.2 on a number line.

Learn how to find the distances between points F = 12.9, E = -5, and D = -10.2 on a number line. This problem demonstrates key geometric concepts such as calculating absolute value distances between points. Suitable for students in Grades 6-8.

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