Given R (1, -1) and S (6, 4), find the midpoint of segment RS.  Record x + y in grid provided.

The formula for finding the midpoint of a segment between two points \( R(x_1, y_1) \) and \( S(x_2, y_2) \) is given by:

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

For the points \( R(1, -1) \) and \( S(6, 4) \), we can substitute their coordinates into the formula:

\[
\text{Midpoint} = \left( \frac{1 + 6}{2}, \frac{-1 + 4}{2} \right) = \left( \frac{7}{2}, \frac{3}{2} \right)
\]

Now, sum the \( x \)- and \( y \)-coordinates of the midpoint:

\[
x + y = \frac{7}{2} + \frac{3}{2} = \frac{10}{2} = 5
\]

Thus, the value of \( x + y \) is \( 5 \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How can we verify the calculation of the midpoint for any line segment?
2. What is the distance between points \( R(1, -1) \) and \( S(6, 4) \)?
3. How can you find the equation of the line passing through points \( R(1, -1) \) and \( S(6, 4) \)?
4. What is the slope of the line segment connecting points \( R(1, -1) \) and \( S(6, 4) \)?
5. How would you find the midpoint if one of the points was at the origin?

**Tip:** The midpoint formula always provides the average of the coordinates of the two points.

Given R (1, -1) and S (6, 4), find the midpoint of segment RS. Record x + y in grid provided.

Discover how to find the midpoint of the line segment RS with endpoints R(1, -1) and S(6, 4). This problem involves using the midpoint formula to calculate the average of the coordinates. It also includes summing the x and y values of the midpoint. Suitable for students in Grades 6-8.

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