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What is the PREIMAGE of the point (a, b) under a translation by the vector <-3, 5>?

a) (a - 3, b + 5)
b) (a + 3, b - 5)
c) (a - 3, b - 5)
d) (a + 3, b + 5)

User Diaa Sami
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1 Answer

3 votes

Final answer:

The preimage of the point (a, b) under the translation by the vector <-3, 5> is (a + 3, b - 5), which means we reverse the translation by adding 3 to the x-coordinate and subtracting 5 from the y-coordinate.

Step-by-step explanation:

The question asks what the preimage of a point is under a given translation by a vector. A translation moves a point in the plane by a certain distance in a given direction, which is indicated by the translation vector. For the point (a, b) being translated by the vector <-3, 5>, this means we subtract 3 from the x-coordinate (a) and add 5 to the y-coordinate (b) of the original point to get its image after the translation. Therefore, the preimage of the translated point, meaning the original point before the translation, should be reversed: To find the original coordinates, we add 3 to the x-coordinate and subtract 5 from the y-coordinate. The correct answer to the question is then option (b) (a + 3, b - 5).

User Steve Carey
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