To find the distance between the points \((-1, 7)\) and \((-8, 6)\), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, we have:
- \( (x_1, y_1) = (-1, 7) \)
- \( (x_2, y_2) = (-8, 6) \)
Now substitute the coordinates into the distance formula:
\[ d = \sqrt{((-8) - (-1))^2 + (6 - 7)^2} \] \[ = \sqrt{(-8 + 1)^2 + (-1)^2} \] \[ = \sqrt{(-7)^2 + (-1)^2} \] \[ = \sqrt{49 + 1} \] \[ = \sqrt{50} \] \[ = \sqrt{25 \times 2} \] \[ = 5\sqrt{2} \]
Calculating \(5\sqrt{2}\) using the approximate value of \(\sqrt{2} \approx 1.414\):
\[ 5 \times 1.414 \approx 7.07 \]
Rounding \(7.07\) to the nearest tenth gives us approximately \(7.1\).
Therefore, the distance between the points \((-1, 7)\) and \((-8, 6)\) is:
\[ \boxed{7.1} \]