To find the coordinates of point $S(x_2, y_2)$, we can use the midpoint formula. The midpoint formula for two points $R(x_1, y_1)$ and $S(x_2, y_2)$ is:

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

Given that $M(-3, 2)$ is the midpoint and $R(6, 0)$, we can plug these values into the formula:

$\left( \frac{6 + x_2}{2}, \frac{0 + y_2}{2} \right) = (-3, 2)$

This gives two equations:

1. $\frac{6 + x_2}{2} = -3$
2. $\frac{0 + y_2}{2} = 2$

Solve for $x_2$:

$\frac{6 + x_2}{2} = -3$ Multiply both sides by 2: $6 + x_2 = -6$ Subtract 6 from both sides: $x_2 = -12$

Solve for $y_2$:

$\frac{y_2}{2} = 2$ Multiply both sides by 2: $y_2 = 4$

Therefore, the coordinates of point $S$ are:

$S(-12, 4)$

Would you like further details or explanations?

Here are 5 related questions:

1. How would the formula change if $M$ was not the midpoint?
2. Can the midpoint formula be used for 3D coordinates?
3. What is the distance between points $R$ and $S$?
4. How does the midpoint formula relate to vectors?
5. How can you verify that $M$ is indeed the midpoint of $R$ and $S$?

Tip: Always double-check your calculations by substituting back into the original equations.