To find the distance between the points \((-1, 7)\) and \( (6, -5)\), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-1, 7)\) and \((x_2, y_2) = (6, -5)\).
Now, plug in the values:
\[ d = \sqrt{(6 - (-1))^2 + (-5 - 7)^2} \]
Calculating the differences:
\[ d = \sqrt{(6 + 1)^2 + (-5 - 7)^2} \] \[ d = \sqrt{(7)^2 + (-12)^2} \]
Calculate the squares:
\[ d = \sqrt{49 + 144} \] \[ d = \sqrt{193} \]
Thus, the distance between the points \((-1, 7)\) and \( (6, -5)\) is
\[ \sqrt{193} \]
If you want a decimal approximation, it is approximately \(13.89\).