We are given that the midpoint $M(4.5, 6.5)$ and one endpoint $R(3, 20)$ of a line segment $RS$ are provided. We need to find the coordinates of the other endpoint $S(x, y)$.

The formula for the midpoint $M$ of a line segment with endpoints $R(x_1, y_1)$ and $S(x_2, y_2)$ is:

$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

We know the midpoint $M(4.5, 6.5)$ and one endpoint $R(3, 20)$. Let the coordinates of the other endpoint $S$ be $(x, y)$. Using the midpoint formula, we can set up the following system of equations:

$\frac{3 + x}{2} = 4.5 \quad \text{(for the x-coordinate)}$ $\frac{20 + y}{2} = 6.5 \quad \text{(for the y-coordinate)}$

Step 1: Solve for $x$ from the first equation

$\frac{3 + x}{2} = 4.5$ Multiply both sides by 2: $3 + x = 9$ Subtract 3 from both sides: $x = 6$

Step 2: Solve for $y$ from the second equation

$\frac{20 + y}{2} = 6.5$ Multiply both sides by 2: $20 + y = 13$ Subtract 20 from both sides: $y = -7$

Thus, the coordinates of the other endpoint $S$ are $\boxed{(6, -7)}$.

---

Would you like more details on the midpoint formula or how I solved this? Or do you have another question?

Here are some related questions you can explore:

1. What is the formula for the distance between two points on the coordinate plane?
2. How do you calculate the midpoint when both endpoints have negative coordinates?
3. What are the properties of a line segment in geometry?
4. How do you find the midpoint of a line segment in 3D space?
5. Can the midpoint formula be applied to more than two points?

Tip: Always check that the midpoint is correct by plugging the calculated endpoint coordinates back into the midpoint formula to verify.