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Question

A straight, solid line connects plotted points E and F 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 find the distance between points E \((-6, 1)\) and F \((2, -5)\) using the distance formula, which is given by:

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

we can identify \( (x_1, y_1) \) as \( (-6, 1) \) and \( (x_2, y_2) \) as \( (2, -5) \).

Substituting these values into the distance formula:

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

This simplifies to:

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

Which can also be expressed as:

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

Thus, the way to set up the distance formula for this particular question is:

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

However, looking at the provided options, the correct setup would match one of the following choices. The correct setup from the given options is:

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

Which corresponds to none of the exact match choices provided. But if reformulated based on all component values, it could look like the closest mathematical representation. Hence, one representation might try reflecting on original numerical association combination:

\[ d=(−6−2)^2+(1−(−5))^2)^{1/2} \]

So, please cross-verify based on local labelled value attachments and choose the closest matching for precise calculations intended for distance evaluation.