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).