To find the length between the points \((-1, 6)\) and \((5, -2)\), we can apply the Pythagorean Theorem, which can be expressed using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).
Substituting the values into the formula, we have:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]
Calculating the differences:
\[ d = \sqrt{(5 + 1)^2 + (-2 - 6)^2} \]
\[ = \sqrt{(6)^2 + (-8)^2} \]
Now calculate the squares:
\[ = \sqrt{36 + 64} \]
\[ = \sqrt{100} \]
Finally, take the square root:
\[ d = 10 \]
The length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
Thus, the final answer is:
10