Asked by willy wonkas messed up chocolate
On this coordinate plane, point A is translated into point A′ . Which functions give the two translations? (1 point) Responses f(x)=x+2 and g(y)=y+5 f left parenthesis x right parenthesis equals x plus 2 and g left parenthesis y right parenthesis equals y plus 5 f(x)=x+5 and g(y)=y+2 f left parenthesis x right parenthesis equals x plus 5 and g left parenthesis y right parenthesis equals y plus 2 f(x)=x−5 and g(y)=y−2 f left parenthesis x right parenthesis equals x minus 5 and g left parenthesis y right parenthesis equals y minus 2 f(x)=x+6 and g(y)=y+3
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GPT-4o mini
To determine which functions represent the translations of point A to point A′, we need to analyze the translations in terms of the x-coordinates and y-coordinates.
Each function can be interpreted as follows:
- The function \( f(x) \) indicates a translation of the x-coordinate.
- The function \( g(y) \) indicates a translation of the y-coordinate.
If the translation involves moving the point to the right, \( f(x) \) would involve adding a positive number. If it involves moving to the left, it would involve subtracting a positive number.
Similarly, for \( g(y) \):
- A positive number added indicates a movement upwards (translation in the positive y direction).
- A negative number (subtracted) indicates a movement downwards (translation in the negative y direction).
You need to identify how point A is translated to point A′ by comparing their coordinates:
- If you know the original coordinates of point A and the new coordinates of point A′, you can easily see how much the x and y coordinates have changed.
Without the specific coordinates or the visual representation of point A and point A′, I cannot definitively choose the correct functions. However, you can apply this reasoning by looking at the differences between the coordinates of points A and A′.
If you know the translation offset for the x and y coordinates, you can match it to the appropriate functions.
For example, if point A is translated right by 2 units and up by 5 units, the correct functions would be:
- \( f(x) = x + 2 \)
- \( g(y) = y + 5 \)
Review your specific translation to confirm which option fits.
Each function can be interpreted as follows:
- The function \( f(x) \) indicates a translation of the x-coordinate.
- The function \( g(y) \) indicates a translation of the y-coordinate.
If the translation involves moving the point to the right, \( f(x) \) would involve adding a positive number. If it involves moving to the left, it would involve subtracting a positive number.
Similarly, for \( g(y) \):
- A positive number added indicates a movement upwards (translation in the positive y direction).
- A negative number (subtracted) indicates a movement downwards (translation in the negative y direction).
You need to identify how point A is translated to point A′ by comparing their coordinates:
- If you know the original coordinates of point A and the new coordinates of point A′, you can easily see how much the x and y coordinates have changed.
Without the specific coordinates or the visual representation of point A and point A′, I cannot definitively choose the correct functions. However, you can apply this reasoning by looking at the differences between the coordinates of points A and A′.
If you know the translation offset for the x and y coordinates, you can match it to the appropriate functions.
For example, if point A is translated right by 2 units and up by 5 units, the correct functions would be:
- \( f(x) = x + 2 \)
- \( g(y) = y + 5 \)
Review your specific translation to confirm which option fits.
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