Find the midpoint of the segment with the following endpoints.

left parenthesis, 9, comma, minus, 10, right parenthesis, and , left parenthesis, 1, comma, minus, 6, right parenthesis

(9,−10) and (1,−6)

To find the midpoint of the line segment with endpoints \((9, -10)\) and \((1, -6)\), use the midpoint formula:

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

Given:
- \(x_1 = 9\), \(y_1 = -10\)
- \(x_2 = 1\), \(y_2 = -6\)

Substitute the values into the formula:

\[
\text{Midpoint} = \left( \frac{9 + 1}{2}, \frac{-10 + (-6)}{2} \right)
\]

Simplify each part:

\[
\text{Midpoint} = \left( \frac{10}{2}, \frac{-16}{2} \right)
\]

\[
\text{Midpoint} = \left( 5, -8 \right)
\]

So, the midpoint is \((5, -8)\).

Would you like more details or have any questions?

Here are 5 related questions to further explore the topic:
1. How do you calculate the distance between the midpoint and one of the endpoints?
2. If you know the midpoint and one endpoint, how do you find the other endpoint?
3. How does the midpoint relate to the concept of the average in mathematics?
4. What happens to the midpoint if both endpoints are shifted by the same vector?
5. Can you use the midpoint formula in three-dimensional space, and if so, how?

**Tip:** The midpoint is the average of the coordinates of the endpoints, making it a powerful tool for finding a point that equally divides a segment.

Learn how to find the midpoint of a line segment with endpoints (9, -10) and (1, -6) using the midpoint formula. This problem involves basic coordinate geometry concepts and calculations. Suitable for students in Grades 7-9.

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