To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we can use the distance formula, which is derived from it. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case:
- \((x_1, y_1) = (-1, 6)\)
- \((x_2, y_2) = (5, -2)\)
Now substituting the coordinates into the formula:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]
Calculating the differences:
- \(x_2 - x_1 = 5 - (-1) = 5 + 1 = 6\)
- \(y_2 - y_1 = -2 - 6 = -8\)
Now substitute these values into the distance formula:
\[ d = \sqrt{(6)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]
Thus, the length between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
So, the correct response is:
10