Question
How would you set up the distance formula to find the distance between points E and F .
Possible Answers:
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=(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 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
Possible Answers:
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=(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 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
Answers
GPT-4o mini
To determine the correct setup for the distance formula between points \( E \) and \( F \), you'll need to consider the coordinates of these points. The distance formula is defined as:
\[
d = \sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2}
\]
Where:
- \((x_1, y_1)\) are the coordinates of the first point (\( E \)).
- \((x_2, y_2)\) are the coordinates of the second point (\( F \)).
To choose the correct formula from the provided options, please identify the coordinates of points \( E \) and \( F \). Assuming those coordinates are:
- \( E = (x_1, y_1) \)
- \( F = (x_2, y_2) \)
You can then match them against the formulas. Here's how each option would translate based on that generic form:
1. \( d = \sqrt{(-2 + 6)^2 + (5 + 1)^2} \)
- This uses \((-2)\) and \((5)\) as coordinates for \( E \), and \((6)\) and \((-1)\) for \( F\), which might not be appropriate based on the actual points.
2. \( d = \sqrt{(2 - 6)^2 + (5 - 1)^2} \)
- This implies \( E = (2, 5) \) and \( F = (6, 1) \).
3. \( d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \)
- This implies \( E = (2, 5) \) and \( F = (6, 1)\), which is mathematically equivalent to option 2.
4. \( d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \)
- This implies \( E = (-6, 1) \) and \( F = (2, -5)\).
Once you have the correct coordinates for points \( E \) and \( F \), you can choose the appropriate answer based on the calculated differences in the x and y coordinates. If neither set of points accurately matches \( E \) and \( F\), the options may not apply.
\[
d = \sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2}
\]
Where:
- \((x_1, y_1)\) are the coordinates of the first point (\( E \)).
- \((x_2, y_2)\) are the coordinates of the second point (\( F \)).
To choose the correct formula from the provided options, please identify the coordinates of points \( E \) and \( F \). Assuming those coordinates are:
- \( E = (x_1, y_1) \)
- \( F = (x_2, y_2) \)
You can then match them against the formulas. Here's how each option would translate based on that generic form:
1. \( d = \sqrt{(-2 + 6)^2 + (5 + 1)^2} \)
- This uses \((-2)\) and \((5)\) as coordinates for \( E \), and \((6)\) and \((-1)\) for \( F\), which might not be appropriate based on the actual points.
2. \( d = \sqrt{(2 - 6)^2 + (5 - 1)^2} \)
- This implies \( E = (2, 5) \) and \( F = (6, 1) \).
3. \( d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \)
- This implies \( E = (2, 5) \) and \( F = (6, 1)\), which is mathematically equivalent to option 2.
4. \( d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \)
- This implies \( E = (-6, 1) \) and \( F = (2, -5)\).
Once you have the correct coordinates for points \( E \) and \( F \), you can choose the appropriate answer based on the calculated differences in the x and y coordinates. If neither set of points accurately matches \( E \) and \( F\), the options may not apply.