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 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=(−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=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√ d 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 with E having the coordinates; (-6,1) and F having the coordinates (2,-5)

Answer 1

To find the distance \( d \) between points \( E(-6, 1) \) and \( F(2, -5) \) using the distance formula, we use:

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

Where:
- \( (x_1, y_1) \) are the coordinates of point \( E \).
- \( (x_2, y_2) \) are the coordinates of point \( F \).

Substituting the coordinates:
- \( x_1 = -6 \), \( y_1 = 1 \)
- \( x_2 = 2 \), \( y_2 = -5 \)

The distance formula becomes:

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

This simplifies to:

\[
d = \sqrt{(2 + 6)^2 + (-5 - 1)^2}
\]
\[
d = \sqrt{(8)^2 + (-6)^2}
\]
\[
d = \sqrt{64 + 36}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

Among the provided responses, the correct expression set up should look like this:

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

This option encapsulates both the correct subtraction of coordinates and the usage of the distance formula.