Point F is on line segment start overline, E, G, end overline
EG
. Given E, G, equals, 19EG=19 and E, F, equals, 15, commaEF=15, determine the length start overline, F, G, end overline, .
FG
.

To determine the length of the line segment \( FG \), we can use the fact that \( F \) is on line segment \( EG \). The total length of \( EG \) is the sum of the lengths of \( EF \) and \( FG \).

Given:
- \( EG = 19 \)
- \( EF = 15 \)

We want to find \( FG \).

Since \( EG = EF + FG \), we can substitute the given values into the equation:

\[
19 = 15 + FG
\]

To find \( FG \), subtract \( 15 \) from both sides:

\[
FG = 19 - 15 = 4
\]

So, the length of \( FG \) is \( 4 \) units.

Would you like more details or have any other questions? Here are some related questions you might find useful:

1. If \( F \) is the midpoint of \( EG \), what would the lengths of \( EF \) and \( FG \) be?
2. How would you calculate \( FG \) if you only knew the coordinates of points \( E \), \( F \), and \( G \)?
3. If \( EF = 15 \) and \( FG = 2x + 3 \), find \( x \) when \( EG = 19 \).
4. What happens to the length of \( FG \) if point \( F \) moves closer to point \( G \)?
5. If \( F \) divides \( EG \) in the ratio \( 3:1 \), what are the lengths of \( EF \) and \( FG \)?

**Tip:** When dealing with line segments and points on a line, breaking the problem down into smaller parts, as we did here, can simplify the calculations significantly.

Learn how to calculate the length of line segment FG on line segment EG, given that EF = 15 units and EG = 19 units. Follow a step-by-step solution involving coordinate geometry principles. Suitable for Grades 7-9.

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