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To solve this problem:

We are given that:
- \( RS = 5 \)
- \( QS = 16 \)

Since point \( R \) is on line segment \( QS \), the total length \( QS \) is the sum of \( QR \) and \( RS \). Therefore, we can write the equation:

\[
QS = QR + RS
\]

Substituting the known values:

\[
16 = QR + 5
\]

To find \( QR \), solve for \( QR \):

\[
QR = 16 - 5 = 11
\]

Thus, the length of \( QR \) is **11**.

Would you like any further details or have other questions?

Here are some related questions:
1. What if \( RS \) was longer than \( QS \)?
2. How can we apply this concept to three-dimensional space?
3. If point \( R \) were the midpoint of \( QS \), what would the length of \( QR \) be?
4. How can we use vectors to represent line segments like \( QS \) and \( QR \)?
5. What are some real-world applications of this kind of geometric reasoning?

**Tip:** Always check whether the points are collinear when working with segments on a line.

Point R is on line segment QS. Given RS = 5 and QS = 16, determine the length of QR.

Learn how to determine the length of QR using the Segment Addition Postulate. Given RS = 5 and QS = 16, follow a step-by-step solution to solve for QR. Ideal for students in Grades 6-8.

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