If A(2, 2),B(-4, -4),and C(5, -8) are the ver | vedclass

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(C) Let $M$ be the midpoint of side $AB$. The coordinates of $M$ are given by the midpoint formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{

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$\sqrt{85}$

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(C) Let $M$ be the midpoint of side $AB$. The coordinates of $M$ are given by the midpoint formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$.Substituting the coordinates of $A(2, 2)$ and $B(-4, -4)$:$M = \left( \frac{2 - 4}{2}, \frac{2 - 4}{2} \right) = \left( \frac{-2}{2}, \frac{-2}{2} \right) = (-1, -1)$.The median passing through $C$ is the line segment $CM$. The length of $CM$ is calculated using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.For $C(5, -8)$ and $M(-1, -1)$:$CM = \sqrt{(-1 - 5)^2 + (-1 - (-8))^2} = \sqrt{(-6)^2 + (7)^2} = \sqrt{36 + 49} = \sqrt{85}$.

If $A(2, 2)$,$B(-4, -4)$,and $C(5, -8)$ are the vertices of a triangle,then the length of the median passing through vertex $C$ is:

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