How would you set up the distance formula to find the distance between points E

Question

and F
.

(1 point)
Responses

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

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=(−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−−−−−−−−−−−−−−−√

Answer 1

To set up the distance formula to find the distance between points \( E \) and \( F \), you would use the standard distance formula:

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

Assuming that the coordinates of point \( E \) are \( (x_1, y_1) \) and the coordinates of point \( F \) are \( (x_2, y_2) \), you need to substitute the values accordingly.

If we take the responses you provided and assume:

• Point \( E \) has coordinates \( (-2, 5) \)
• Point \( F \) has coordinates \( (6, 1) \)

Using these points, the correct setup using the distance formula would be:

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

This simplifies to:

\[ d = \sqrt{(6 + 2)^2 + (1 - 5)^2} = \sqrt{(8)^2 + (-4)^2} = \sqrt{64 + 16} = \sqrt{80} \]

So the correct option from your list would be:

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

However, since you provided responses, the closest correct option matches with:

d = (6 - 2)^2 + (1 - 5)^2 (with appropriate values substituted in earlier contexts).

Make sure to clarify the exact coordinates of points \( E \) and \( F \) to validate completely.