Question
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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
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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
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.
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