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. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).
Now plug in the values:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]
Calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\[ x_2 - x_1 = 5 + 1 = 6 \] \[ y_2 - y_1 = -2 - 6 = -8 \]
Now substitute these into the distance formula:
\[ d = \sqrt{(6)^2 + (-8)^2} \]
Calculate the squares:
\[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \]
Now find the square root:
\[ d = 10 \]
Thus, the length between the points \((-1, 6)\) and \( (5, -2)\) is \(10\).
Rounded to the nearest hundredth, the answer remains:
10