To find the distance between the points \((-1, 6)\) and \((5, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).
Substituting the coordinates into the formula:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]
This simplifies to:
\[ d = \sqrt{(5 + 1)^2 + (-2 - 6)^2} \]
\[ d = \sqrt{(6)^2 + (-8)^2} \]
\[ d = \sqrt{36 + 64} \]
\[ d = \sqrt{100} \]
\[ d = 10 \]
Therefore, the length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
The correct answer is:
10