Point S is on line segment start overline, R, T, end overline*RT*. Given R, T, equals, 19*RT*=19 and R, S, equals, 6, comma*RS*=6, determine the length start overline, S, T, end overline, .*ST*.

To determine the length of the line segment \( ST \), we can use the fact that \( S \) is on line segment \( RT \). The total length of \( RT \) is the sum of the lengths of \( RS \) and \( ST \).

Given:
- \( RT = 19 \)
- \( RS = 6 \)

We want to find \( ST \).

Since \( RT = RS + ST \), we can substitute the given values into the equation:

\[
19 = 6 + ST
\]

To find \( ST \), subtract \( 6 \) from both sides:

\[
ST = 19 - 6 = 13
\]

So, the length of \( ST \) is \( 13 \) units.

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

1. If \( S \) is the midpoint of \( RT \), what would the lengths of \( RS \) and \( ST \) be?
2. How would you calculate \( ST \) if you only knew the coordinates of points \( R \), \( S \), and \( T \)?
3. If \( RS = 6 \) and \( ST = 3x + 1 \), find \( x \) when \( RT = 19 \).
4. What happens to the length of \( ST \) if point \( S \) moves closer to point \( R \)?
5. If \( S \) divides \( RT \) in the ratio \( 2:3 \), what are the lengths of \( RS \) and \( ST \)?

**Tip:** In problems involving line segments, knowing how to set up the relationship between the segments, like \( RT = RS + ST \), is crucial for solving for unknown lengths.

Learn how to calculate the length of line segment ST on line segment RT using given lengths RS = 6 and RT = 19. Understand the relationship between line segments and solve for the unknown length ST. Suitable for Grades 9-10 students studying coordinate geometry and segment lengths.

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