To find the distance between the points \((-5, -1)\) and \((7, -8)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) are the coordinates of the first point, and \((x_2, y_2)\) are the coordinates of the second point.
Plugging in the coordinates:
- \((x_1, y_1) = (-5, -1)\)
- \((x_2, y_2) = (7, -8)\)
Now substitute into the formula:
\[ d = \sqrt{(7 - (-5))^2 + (-8 - (-1))^2} \]
Calculating the differences:
\[ 7 - (-5) = 7 + 5 = 12 \] \[ -8 - (-1) = -8 + 1 = -7 \]
Now substitute these back into the distance formula:
\[ d = \sqrt{(12)^2 + (-7)^2} \] \[ d = \sqrt{144 + 49} \] \[ d = \sqrt{193} \]
Now, we need to calculate \(\sqrt{193}\):
\[ \sqrt{193} \approx 13.9 \]
Thus, the distance between the points \((-5, -1)\) and \((7, -8)\) is approximately 13.9.
So the answer is:
13.9