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 the segment with endpoints \((3, 8)\) and \((-7, 5)\), we'll use the midpoint formula:

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

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

Substituting these values into the formula:

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

Simplifying:

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

So, the midpoint of the segment is \(\left(-2, \frac{13}{2}\right)\), or \((-2, 6.5)\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you determine the midpoint of a line segment on a number line?
2. What is the equation of a line that passes through the midpoint and one of the endpoints?
3. Can you calculate the distance from the midpoint to each endpoint?
4. How does the midpoint relate to the concept of symmetry in geometry?
5. What happens to the midpoint if you scale the line segment by a factor?

**Tip:** It's helpful to write down all intermediate steps when using formulas, as it can prevent small mistakes and clarify your thought process.

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

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