To calculate the length of the median drawn from vertex $C(-8, -6)$ to the side $AB$, follow these steps:

Step 1: Find the midpoint of side $AB$

The coordinates of $A$ and $B$ are: $A(-8, 2), \, B(-2, -6)$ The midpoint formula is: $\text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ Substituting the coordinates of $A$ and $B$: $\text{Midpoint of } AB = \left(\frac{-8 + (-2)}{2}, \frac{2 + (-6)}{2}\right) = \left(\frac{-10}{2}, \frac{-4}{2}\right) = (-5, -2)$

Step 2: Calculate the distance between $C(-8, -6)$ and the midpoint of $AB$

The formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substituting $C(-8, -6)$ and the midpoint of $AB(-5, -2)$: $\text{Distance} = \sqrt{((-5) - (-8))^2 + ((-2) - (-6))^2}$ $\text{Distance} = \sqrt{(3)^2 + (4)^2}$ $\text{Distance} = \sqrt{9 + 16} = \sqrt{25} = 5$

Final Answer:

The length of the median drawn from vertex $C$ to side $AB$ is: $\boxed{5 \, \text{units}}$

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Would you like more details or further clarifications? Here are 5 related questions to expand your understanding:

1. How do you find the centroid of a triangle using its vertices?
2. What is the formula for calculating the length of a median in a triangle when all vertices are known?
3. How can the area of triangle $ABC$ be calculated using its vertices?
4. What are the properties of medians in a triangle?
5. How is the distance formula derived from the Pythagorean theorem?

Tip: Always verify your calculations by double-checking the midpoint and distance formula for accuracy.