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 the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's assign the coordinates:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 5\)
- \(y_2 = -2\)
Now, we will plug these values into the distance formula:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]
Calculating \(5 - (-1)\):
\[ 5 + 1 = 6 \]
Calculating \(-2 - 6\):
\[ -2 - 6 = -8 \]
Now substituting these values back into the formula, we have:
\[ d = \sqrt{(6)^2 + (-8)^2} \]
Calculating \(6^2\) and \((-8)^2\):
\[ 6^2 = 36 \] \[ (-8)^2 = 64 \]
Now summing these:
\[ d = \sqrt{36 + 64} = \sqrt{100} \]
Finally, taking the square root gives us:
\[ d = 10 \]
Thus, the distance between the points \((-1, 6)\) and \( (5, -2)\) is \(10\). Rounding is not necessary here as it is a whole number.
Final Answer: 10