The endpoints of CD are C(-8, - 6) and D(-4, 10).

To analyze the line segment CD with endpoints C(-8, -6) and D(-4, 10), we can find several key properties:

### 1. **Length of CD**
The length of the line segment can be calculated using the distance formula:
\[
\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the coordinates of C(-8, -6) and D(-4, 10):
\[
\text{Length} = \sqrt{(-4 - (-8))^2 + (10 - (-6))^2} = \sqrt{(4)^2 + (16)^2} = \sqrt{16 + 256} = \sqrt{272} = 4\sqrt{17} \approx 16.49
\]

### 2. **Midpoint of CD**
The midpoint of the line segment can be found using the midpoint formula:
\[
\text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]
Substituting the coordinates of C(-8, -6) and D(-4, 10):
\[
\text{Midpoint} = \left(\frac{-8 + (-4)}{2}, \frac{-6 + 10}{2}\right) = \left(\frac{-12}{2}, \frac{4}{2}\right) = (-6, 2)
\]

### 3. **Slope of CD**
The slope of the line segment is calculated using the slope formula:
\[
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of C(-8, -6) and D(-4, 10):
\[
\text{Slope} = \frac{10 - (-6)}{-4 - (-8)} = \frac{16}{4} = 4
\]

### Summary
- **Length of CD**: \( 4\sqrt{17} \) or approximately 16.49 units
- **Midpoint of CD**: (-6, 2)
- **Slope of CD**: 4

Would you like any further details or have any questions?

Here are some related questions:
1. How do you find the equation of the line that passes through points C and D?
2. What is the perpendicular slope to the line CD?
3. How do you calculate the area of a triangle formed with another point and this line segment?
4. What are the x and y intercepts of the line through CD?
5. How does the distance from a point to a line compare with the segment length?

**Tip:** The distance formula is essentially the Pythagorean Theorem applied to the difference in coordinates.

Explore the properties of the line segment CD with endpoints at C(-8, -6) and D(-4, 10). Calculate its length, find the midpoint, and determine its slope using detailed step-by-step solutions. Suitable for students in Grades 9-12.

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