To find the midpoint $M$ of a line segment with endpoints $R(x_1, y_1)$ and $S(x_2, y_2)$, you can use the midpoint formula:

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

Given the endpoints $R(2, 7)$ and $S(10, 9)$, substitute these values into the formula:

$M = \left(\frac{2 + 10}{2}, \frac{7 + 9}{2}\right)$

Simplify the calculations:

$M = \left(\frac{12}{2}, \frac{16}{2}\right) = (6, 8)$

So, the midpoint $M$ of $RS$ is $\mathbf{(6, 8)}$.

Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. How do you find the length of the segment RS?
2. What is the slope of the line passing through R and S?
3. How would the midpoint change if one of the coordinates were negative?
4. Can you generalize the midpoint formula for 3-dimensional space?
5. How do you derive the midpoint formula?

Tip: The midpoint formula is particularly useful in geometry problems involving bisectors and symmetry.