To determine the distance between the points \((-1, -4)\) and \((-9, -8)\), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the points \((x_1, y_1) = (-1, -4)\) and \((x_2, y_2) = (-9, -8)\), we can substitute these values into the formula:
\[ d = \sqrt{((-9) - (-1))^2 + ((-8) - (-4))^2} \]
Simplifying the differences:
\[ d = \sqrt{(-9 + 1)^2 + (-8 + 4)^2} \] \[ d = \sqrt{(-8)^2 + (-4)^2} \] \[ d = \sqrt{64 + 16} \] \[ d = \sqrt{80} \]
Thus, the distance between the points \((-1, -4)\) and \((-9, -8)\) is \(\sqrt{80}\) units.
Therefore, the correct answer is:
square root of 80 units.