Final answer:
The image of the point Y(-4, 7) under the translation <3, -5> is found by adding the translation vector to the original point's coordinates, resulting in the point Y(-1, 2), which corresponds to Option 3.
Step-by-step explanation:
The question involves finding the image of a point after a translation in a coordinate plane. The point Y(-4, 7) is being translated by the vector <3, -5>. To find the image of the point, we add the translation vector to the original coordinates.
To perform this operation, we take the x-coordinate of Y which is -4 and add 3 to it, getting -1. Then, we take the y-coordinate which is 7 and subtract 5 from it, getting 2. Therefore, the translated point is Y(-1, 2).
The correct answer is Option 3: Y (-1,2).