To find the midpoint of a line segment joining two points, you use the midpoint formula:

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

Given the points $R(3, 3)$ and $S(-2, 6)$:

• $x_1 = 3$, $y_1 = 3$
• $x_2 = -2$, $y_2 = 6$

Now, substitute these values into the formula:

$\text{Midpoint} = \left( \frac{3 + (-2)}{2}, \frac{3 + 6}{2} \right)$

Simplify the expressions:

$\text{Midpoint} = \left( \frac{1}{2}, \frac{9}{2} \right)$

Therefore, the midpoint is:

$\left( \frac{1}{2}, \frac{9}{2} \right)$

Do you want more details or have any questions?

Here are some related questions to consider:

1. How do you find the distance between the points $R$ and $S$?
2. What is the slope of the line passing through $R$ and $S$?
3. How would you find the equation of the line passing through $R$ and $S$?
4. Can you verify the midpoint by finding the average of the x-coordinates and y-coordinates separately?
5. What happens to the midpoint if both points are shifted by the same amount?

Tip: Always double-check your midpoint calculations by averaging the x-coordinates and y-coordinates separately.