Use the given endpoint R and midpoint M of segment RS to find the coordinates of the other endpoint S. R: ( 7, -17) M: (-2, 3)

To find the coordinates of the other endpoint \( S(x, y) \) of the segment \( RS \) when given the endpoint \( R(x_1, y_1) \) and the midpoint \( M(x_m, y_m) \), you can use the midpoint formula:

\[
M(x_m, y_m) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Given:
- \( R(x_1, y_1) = (7, -17) \)
- \( M(x_m, y_m) = (-2, 3) \)

Let's denote the coordinates of the other endpoint \( S \) as \( (x_2, y_2) \).

Using the midpoint formula:
\[
x_m = \frac{x_1 + x_2}{2} \quad \text{and} \quad y_m = \frac{y_1 + y_2}{2}
\]

Substitute the values for \( x_m \), \( y_m \), \( x_1 \), and \( y_1 \):

\[
-2 = \frac{7 + x_2}{2} \quad \text{and} \quad 3 = \frac{-17 + y_2}{2}
\]

Now, solve for \( x_2 \) and \( y_2 \):

### Solve for \( x_2 \):
\[
-2 = \frac{7 + x_2}{2}
\]
Multiply both sides by 2:
\[
-4 = 7 + x_2
\]
Subtract 7 from both sides:
\[
x_2 = -11
\]

### Solve for \( y_2 \):
\[
3 = \frac{-17 + y_2}{2}
\]
Multiply both sides by 2:
\[
6 = -17 + y_2
\]
Add 17 to both sides:
\[
y_2 = 23
\]

### Therefore, the coordinates of the other endpoint \( S \) are \( \boxed{(-11, 23)} \).

Would you like to explore any further details or have any other questions?

Here are 5 related questions:
1. How would you find the distance between the endpoints \( R \) and \( S \)?
2. What is the equation of the line passing through points \( R \) and \( S \)?
3. How do you determine if two segments are perpendicular given their endpoints?
4. Can you verify that the calculated point \( S \) is correct using the midpoint formula?
5. What would be the coordinates of the midpoint if the endpoints were swapped?

**Tip:** Always check your final answer by substituting it back into the original equation to ensure accuracy.

Learn how to find the coordinates of endpoint S of segment RS using the midpoint formula. Given the endpoint R (7, -17) and midpoint M (-2, 3), calculate the coordinates of S. Includes step-by-step solution and practice problems. Suitable for Grades 9-10.

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