Final answer:
The coordinates (1, 4) translated to (-1, -1) indicate a translation of 2 units left and 5 units down, resulting in the translation vector (-2, -5).
Step-by-step explanation:
The original point (1, 4) was translated to point N' (-1, -1). The translation involves moving the point horizontally from 1 to -1 and vertically from 4 to -1. To find the translation, we subtract the coordinates of N' from the original point's coordinates.
Translation in x-direction: -1 - 1 = -2 (move 2 units to the left)
Translation in y-direction: -1 - 4 = -5 (move 5 units down)
The translation vector is thus (-2, -5), which means the point underwent a translation of 2 units to the left and 5 units down. Translation in mathematics is moving every point of a shape in the same direction and by the same amount.