Find the midpoint of the segment with the following endpoints.

left parenthesis, 2, comma, 10, right parenthesis, and , left parenthesis, minus, 8, comma, 7, right parenthesis

(2,10) and (−8,7)

To find the midpoint of the segment with endpoints \((2, 10)\) and \((-8, 7)\), we use the midpoint formula:

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

Given:

- \(x_1 = 2\), \(y_1 = 10\)
- \(x_2 = -8\), \(y_2 = 7\)

Substitute these values into the formula:

\[
\text{Midpoint} = \left( \frac{2 + (-8)}{2}, \frac{10 + 7}{2} \right)
\]

Simplify each part:

\[
\text{Midpoint} = \left( \frac{-6}{2}, \frac{17}{2} \right)
\]

\[
\text{Midpoint} = \left( -3, \frac{17}{2} \right)
\]

Thus, the midpoint of the segment is \(\left(-3, \frac{17}{2}\right)\).

Would you like further details or have any questions?

Here are some related questions you might find useful:
1. How do you determine the equation of a line given two endpoints?
2. How can the midpoint formula be used in three dimensions?
3. What is the distance between the midpoint and one of the endpoints?
4. How does the midpoint relate to the centroid of a triangle?
5. Can the midpoint formula be used in geometry problems involving circles?

**Tip:** The midpoint is always equidistant from both endpoints, making it a valuable tool in various geometric constructions and proofs.

Learn how to find the midpoint of a line segment with endpoints (2, 10) and (-8, 7) using the midpoint formula. Understand the steps involved in calculating the midpoint coordinates. Suitable for students in Grades 8-10.

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