To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) is the first point and \((x_2, y_2)\) is the second point.
Substituting the coordinates:
\((x_1, y_1) = (-1, 6)\)
\((x_2, y_2) = (5, -2)\)
Now, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\[ x_2 - x_1 = 5 - (-1) = 5 + 1 = 6 \] \[ y_2 - y_1 = -2 - 6 = -8 \]
Now substitute these results into the distance formula:
\[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]
Thus, the length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
Therefore, the correct response is 10.