What is the center of segment MN given M(3, -1) ad N(7, -5)?
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The center of a segment (also known as the midpoint) between two points \( M(x_1, y_1) \) and \( N(x_2, y_2) \) can be calculated using the midpoint formula:

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

For the points \( M(3, -1) \) and \( N(7, -5) \):

\[
\text{Midpoint} = \left( \frac{3 + 7}{2}, \frac{-1 + (-5)}{2} \right)
               = \left( \frac{10}{2}, \frac{-6}{2} \right)
               = (5, -3)
\]

Thus, the center (midpoint) of segment MN is \( (5, -3) \).

Would you like further details on the process?

Here are 5 related questions:
1. How do you find the distance between two points in a coordinate plane?
2. How is the midpoint formula related to the concept of averages?
3. What is the slope of the line segment connecting points M and N?
4. Can the midpoint formula be extended to three dimensions?
5. How would you verify that two segments are congruent using midpoints?

**Tip:** When calculating midpoints, you're essentially finding the average of the x-coordinates and the average of the y-coordinates of the two points.

What is the center of segment MN given M(3, -1) and N(7, -5)?

Learn how to find the midpoint of segment MN with given points M(3, -1) and N(7, -5) using the midpoint formula. This detailed step-by-step solution is ideal for students in Grades 6-8, covering key concepts in coordinate geometry.

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