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To find the midpoint \( M \) of line segment \( \overline{QR} \), given the endpoints \( Q(5, 2) \) and \( R(3, 8) \), we use the midpoint formula:

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

Here, the coordinates of point \( Q \) are \( (x_1, y_1) = (5, 2) \), and the coordinates of point \( R \) are \( (x_2, y_2) = (3, 8) \).

Let's calculate the midpoint \( M \):

\[
M_x = \frac{5 + 3}{2} = \frac{8}{2} = 4
\]
\[
M_y = \frac{2 + 8}{2} = \frac{10}{2} = 5
\]

Thus, the midpoint \( M \) is \( (4, 5) \).

Do you have any questions or would you like further details on this solution?

Here are 5 related questions to expand on this topic:
1. How do you find the midpoint if the coordinates are negative?
2. Can the midpoint formula be applied in three-dimensional space?
3. How do you find the distance between two points using their coordinates?
4. What is the relationship between the midpoint and the slope of a line segment?
5. How does the midpoint change if one endpoint is shifted by a certain distance?

**Tip:** The midpoint formula always gives the average of the x-coordinates and y-coordinates of the two points, which helps you locate the point that is exactly halfway between them.

QR has endpoints at Q(5, 2) and R(3, 8). Find the midpoint M of QR.

Learn how to find the midpoint of a line segment with endpoints Q(5, 2) and R(3, 8) using the midpoint formula. This problem covers key concepts in coordinate geometry and is suitable for students in Grades 6-8.

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