To find the distance between points E \((-6, 1)\) and F \((2, -5)\) using the distance formula, we use the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, \((x_1, y_1) = (-6, 1)\) and \((x_2, y_2) = (2, -5)\).
Substituting these coordinates into the distance formula, we have:
\[
d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2}
\]
Which simplifies to:
\[
d = \sqrt{(2 + 6)^2 + (-5 - 1)^2}
\]
\[
d = \sqrt{(8)^2 + (-6)^2}
\]
\[
d = \sqrt{64 + 36}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
Therefore, the correct setup of the distance formula for points \(E\) and \(F\) is:
**d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2}**
Among the options provided, the correct response would be:
**d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2}**.