To find the length between the points \((-1, 6)\) and \( (5, -2)\) using the Pythagorean Theorem, we can treat the distance as the hypotenuse of a right triangle.
First, we need to find the differences in the x-coordinates and y-coordinates:
- The change in x (Δx) = \(5 - (-1) = 5 + 1 = 6\)
- The change in y (Δy) = \(-2 - 6 = -8\)
Now we can apply the Pythagorean Theorem:
\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \] \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]
Thus, the length between the points \((-1, 6)\) and \( (5, -2)\) is \(10\).
The correct answer is 10.