Question

How would you set up the distance formula to find the distance between points E and F . (1 point) Responses d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√ d is equal to square root of open paren negative 6 minus 2 close paren squared plus open paren 1 minus negative 5 close paren squared end root d=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 2 minus 6 close paren squared plus open paren 5 minus 1 close paren squared end root d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
E is at (-6, 1)
F is at (2, -5)

Answer 1

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:

1. Calculate \( 2 - (-6) = 2 + 6 = 8 \)
2. 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.