Find the midpoint of the segment with the following endpoints.

left parenthesis, 3, comma, 8, right parenthesis, and , left parenthesis, minus, 7, comma, 5, right parenthesis

(3,8) and (−7,5)

To find the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), 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 \((3, 8)\) and \((-7, 5)\):

- \(x_1 = 3\), \(y_1 = 8\)
- \(x_2 = -7\), \(y_2 = 5\)

Now, apply the midpoint formula:

\[
\text{Midpoint} = \left( \frac{3 + (-7)}{2}, \frac{8 + 5}{2} \right)
\]

Simplifying each part:

\[
\text{Midpoint} = \left( \frac{-4}{2}, \frac{13}{2} \right)
\]

\[
\text{Midpoint} = \left( -2, \frac{13}{2} \right)
\]

So, the midpoint of the segment is \(\left(-2, \frac{13}{2}\right)\).

Would you like further details on this or have any questions?

Here are some related questions you might find interesting:
1. How do you find the distance between two points?
2. What is the slope of the line segment with these endpoints?
3. How would the midpoint change if one of the coordinates was negative?
4. Can you use the midpoint formula to divide a segment into a different ratio?
5. How does the midpoint formula relate to the concept of averages?

**Tip:** The midpoint formula is essentially finding the average of the x-coordinates and y-coordinates separately.

Learn how to find the midpoint of a line segment with endpoints (3,8) and (-7,5) using the midpoint formula. This problem covers coordinate geometry concepts and the application of the midpoint formula. Suitable for students in Grades 7-9.

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