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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=((−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=(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

Answer 1

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

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

Where \((x_1, y_1)\) are the coordinates of point E and \((x_2, y_2)\) are the coordinates of point F. Substituting in the specific coordinates:

• \(x_1 = -6\), \(y_1 = 1\)
• \(x_2 = 2\), \(y_2 = -5\)

The distance formula setup would be:

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

This simplifies to:

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

None of the provided responses are exactly correct because they contain errors in the setup. However, the closest response, employing the correct adjustments, would be:

d = square root of open paren 2 minus negative 6 close paren squared plus open paren negative 5 minus 1 close paren squared end root

Since the intended expression and calculations involve:

• \(x_2 - x_1 = 2 - (-6) = 2 + 6 = 8\)
• \(y_2 - y_1 = -5 - 1 = -6\)

To sum it all up, the official option setup was not available, but the closely matching answer with positioning correction should be indicated.