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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 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

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

Answer 1

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

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

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

Plugging in the values:

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

This can be rewritten as:

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

Thus, the correct response based on the options provided would be:

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

(Note: The original scenario describes point E as \((-6,1)\) and point F as \((2,-5)\), so this interpretation aims to align with the possible response that correctly uses the coordinates.)