Find the midpoint of the segment with the following endpoints.

left parenthesis, minus, 9, comma, minus, 10, right parenthesis, and , left parenthesis, 0, comma, minus, 7, right parenthesis

(−9,−10) and (0,−7)

To find the midpoint of a line segment with endpoints \((-9, -10)\) and \((0, -7)\), you can use the midpoint formula:

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

Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

Given:
- \(x_1 = -9\), \(y_1 = -10\)
- \(x_2 = 0\), \(y_2 = -7\)

Substitute the values into the formula:

\[
\text{Midpoint} = \left( \frac{-9 + 0}{2}, \frac{-10 + (-7)}{2} \right)
\]

Simplify each part:

\[
\text{Midpoint} = \left( \frac{-9}{2}, \frac{-17}{2} \right)
\]

Thus, the midpoint is:

\[
\left( -\frac{9}{2}, -\frac{17}{2} \right) \text{ or } \left( -4.5, -8.5 \right)
\]

Would you like more details or have any questions?

Here are 5 related questions to further explore the topic:
1. How do you find the midpoint if one endpoint and the midpoint are known?
2. What is the significance of the midpoint in coordinate geometry?
3. How can you determine the length of the segment using its endpoints?
4. How would the midpoint change if the segment was translated 5 units to the right?
5. What is the relationship between the midpoint and the line segment's symmetry?

**Tip:** The midpoint of a line segment divides it into two equal parts, making it a useful tool in geometric constructions and proofs.

Learn how to find the midpoint of a line segment with endpoints (−9,−10) and (0,−7) using the midpoint formula. This problem involves coordinate geometry and provides a step-by-step solution. Suitable for students in Grades 6-8.

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