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Question

A straight, solid line connects plotted points E (-6,1) and F (2,-5) on a coordinate plane. The line slopes downward from left to right. Point E is left parenthesis negative 6 comma 1 right parenthesis. Point F is left parenthesis 2 comma negative 5 right parenthesis.

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−−−−−−−−−−−−−−−−−−√
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
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Answer 1

To set up the distance formula for finding the distance between points E (-6, 1) and F (2, -5), you would use the distance formula:

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

Here, for point E, \( (x_1, y_1) = (-6, 1) \) and for point F, \( (x_2, y_2) = (2, -5) \).

Substituting these values into the formula, you have:

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

Simplifying that gives you:

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

The correct setup based on the options provided is:

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

However, it seems there's a transcription error in the options provided. Based on correction, the most closely aligned would resemble the correct setup after simplifying:

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

Thus, the best option is:

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

This matches with option:

d = (2−(-6))^2+(1−(-5))^2−−−−−−−−−−−−−−−−−−−√