To find the distance between the points \( E(-6, 1) \) and \( F(2, -5) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (-6, 1) \) and \( (x_2, y_2) = (2, -5) \).
Substituting the values into the formula, we get:
\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]
Simplifying the expression inside the square root:
- Calculate \( 2 - (-6) = 2 + 6 = 8 \)
- Calculate \( -5 - 1 = -6 \)
Now plug these into the distance formula:
\[ d = \sqrt{(8)^2 + (-6)^2} \]
Calculate the squares:
\[ d = \sqrt{64 + 36} \]
Add them together:
\[ d = \sqrt{100} \]
Finally, take the square root:
\[ d = 10 \]
So, the distance between points E and F is \( 10 \).
Now, looking at your given responses, the correct distance formula setup resembles:
\(d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2}\)
This version corresponds to the rearrangement of the points but correctly applies the distance formula based on the coordinates provided.