Question

How would you set up the distance formula to find the distance between points E and F.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ad=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√%0D%0Ad is equal to square root of open paren negative 2 plus 6 close paren squared plus open paren 5 plus 1 close paren squared end root%0D%0A%0D%0Ad=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√%0D%0Ad 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%0D%0A%0D%0Ad=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√%0D%0Ad 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%0D%0A%0D%0Ad=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√%0D%0Ad 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

Answer 1

To find the distance between two points \( E(x_1, y_1) \) and \( F(x_2, y_2) \) using the distance formula, you use the following formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

To set it up correctly, you just need to substitute the coordinates of points E and F into the formula.

Given your potential responses, let's select the correct one.

If we let \( E = (-2, 5) \) and \( F = (6, -1) \):

1. \( x_1 = -2 \), \( y_1 = 5 \)
2. \( x_2 = 6 \), \( y_2 = -1 \)

Using the distance formula:

\[
d = \sqrt{(6 - (-2))^2 + (-1 - 5)^2}
\]
This simplifies to:

\[
d = \sqrt{(6 + 2)^2 + (-6)^2}
\]
Which leads to:

\[
d = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10
\]

From the options provided:

- The correct form should be:
\[
d = \sqrt{(6 - (-2))^2 + (-1 - 5)^2}
\]
Thus, the correct response setting up the distance formula would be:
\[
d = \sqrt{(6 + 2)^2 + (-1 - 5)^2}
\]

So, your answer is the response where:
\[
d = \sqrt{(6 - (-2))^2 + (-1 - 5)^2}
\] (if this option is available).