Find the midpoint of the segment with the following endpoints.

left parenthesis, 6, comma, 7, right parenthesis, and , left parenthesis, 2, comma, 1, right parenthesis

(6,7) and (2,1)

To find the midpoint of the segment with endpoints \((6, 7)\) and \((2, 1)\), you can use the midpoint formula:

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

Given the endpoints \((6, 7)\) and \((2, 1)\), let's calculate:

1. Calculate the average of the \(x\)-coordinates:
   \[
   \frac{6 + 2}{2} = \frac{8}{2} = 4
   \]

2. Calculate the average of the \(y\)-coordinates:
   \[
   \frac{7 + 1}{2} = \frac{8}{2} = 4
   \]

So, the midpoint of the segment is:

\[
(4, 4)
\]

Would you like further details or have any questions?

Here are 5 related questions you might be interested in:
1. How would the midpoint change if the segment's endpoints were moved?
2. How do you find the midpoint in a coordinate plane with negative coordinates?
3. Can the midpoint formula be used for a line segment in a three-dimensional space?
4. How do you find the distance between the midpoint and one of the endpoints?
5. How does the concept of a midpoint apply to geometric shapes like triangles and quadrilaterals?

**Tip:** When using the midpoint formula, always ensure that you're correctly averaging both the \(x\) and \(y\) coordinates separately to avoid errors.

Discover how to find the midpoint of a segment with endpoints (6, 7) and (2, 1) using the midpoint formula step-by-step. This problem involves coordinate geometry and is suitable for Grades 6-8 students.

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