Final answer:
The translation of the point (3,-2) to (1,0) is represented by the function Translate: (x,y) to (x-2, y+2), which signifies a move 2 units to the left and 2 units upward on a cartesian plane.
Step-by-step explanation:
To describe the translation of the point (3,-2) to its image (1,0), we observe the changes in the x and y coordinates separately. The x-coordinate moves from 3 to 1 which is a decrease of 2 units. Similarly, the y-coordinate moves from -2 to 0 which is an increase of 2 units. Therefore, the translation can be represented as moving each point 2 units left and 2 units up, which would be expressed in function notation as Translate: (x, y) to (x - 2, y + 2).
Using cartesian coordinates and an understanding of translations, we can easily visualize this movement on a 2-dimensional grid. A point is shifted horizontally and vertically without rotation or change of size. Consideration of translations in three-dimensional space adds the possibility of moving along the z-axis, which is not applicable to this particular question.
The student initially mentioned Translate: (x,y) to (x-2,y-2) which is an incorrect statement for this translation. The accurate representation of the translation described is (x-2, y+2).