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\# is the image of after a translation along the rule . What are the coordinates of pre-image ?
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Q. \# is the image of after a translation along the rule . What are the coordinates of pre-image ?
- Understand translation rule: First, let's understand the translation rule given: . This means that for any point , the -coordinate is decreased by and the -coordinate is squared and then decreased by to get the image point.
- Find pre-image point: We are given the image point as . To find the pre-image , we need to reverse the translation rule. This means we need to add to the -coordinate of the image and find the square root of the -coordinate of the image plus .
- Reverse translation for -coordinate: Let's apply the reverse translation to the -coordinate of the image point. We add to the -coordinate of the image point: .
- Reverse translation for y-coordinate: Now, let's apply the reverse translation to the y-coordinate of the image point. We first add to the y-coordinate of the image point: . Since we cannot take the square root of a negative number in the set of real numbers, there is a math error here. We cannot proceed with finding the square root of as it would result in an imaginary number, which is not applicable in this context.
