Given directed line segment RT below, find the coordinates of S such that the ratio of RS to ST is 5:1. Plot point S

Let's break down the problem:

### Given:
- The directed line segment \( \overrightarrow{RT} \).
- We need to find the coordinates of point \( S \) such that the ratio of \( RS \) to \( ST \) is 5:1.

### Steps to solve:
1. **Let the coordinates of \( R \) be \( R(x_1, y_1) \) and \( T \) be \( T(x_2, y_2) \).**
   
2. **The formula to find a point that divides a line segment in a given ratio (internal division)** is:
   \[
   \left( \frac{m \cdot x_2 + n \cdot x_1}{m+n}, \frac{m \cdot y_2 + n \cdot y_1}{m+n} \right)
   \]
   Where:
   - \( m:n \) is the ratio in which the point divides the line segment.
   - In this case, \( m = 5 \) and \( n = 1 \) (since \( RS : ST = 5:1 \)).

3. **Substitute the coordinates of \( R \) and \( T \) into the formula to find the coordinates of \( S \).**

If you can provide the coordinates of points \( R \) and \( T \), I can help you calculate the exact coordinates of \( S \) and assist in plotting.

Would you like to proceed with the calculation or provide the coordinates?

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### 5 Related Questions:
1. How is the midpoint of a line segment calculated?
2. What is the formula for dividing a line segment externally?
3. Can the same ratio concept be applied in three-dimensional space?
4. What happens if the ratio is negative in a directed segment?
5. How do you find the distance between two points on a coordinate plane?

**Tip**: Always double-check the ratio given in the problem as it dictates how to divide the line segment.

Given directed line segment RT below, find the coordinates of S such that the ratio of RS to ST is 5:1. Plot point S.

Learn how to find the coordinates of point S that divides the directed line segment RT in the ratio 5:1 using the internal division formula. Understand the steps and concepts, including ratios and coordinate geometry. Suitable for students in Grades 9-11.

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