M(-3,2) is the midpoint of RS, and R and R has coordinates (6,0). What are the coordinates of S?

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.

M(-3,2) is the midpoint of RS, and R has coordinates (6,0). What are the coordinates of S?

Learn how to find the coordinates of point S given that M(-3,2) is the midpoint of RS, and R has coordinates (6,0). This problem uses the midpoint formula and linear equations, making it suitable for students in Grades 7-9.

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