Final answer:
The pre-image point A, before being translated to point B(-8, -2), is found by reversing the translation. This involves adding 3 to the x-coordinate and 1 to the y-coordinate of point B, resulting in point A(-5, -1).
Step-by-step explanation:
The student is asking about the coordinates of the original point (pre-image point) before a translation was applied to get point B(-8, -2). A translation moves every point of a figure or a space by the same amount in a given direction. To find the original point A, you perform the inverse of the translation that was applied to point B.
Since point B is the result of translating point A left 3 units and down 1 unit, we must do the opposite to find point A:
- Move right (add to the x-coordinate) by 3 units.
- Move up (add to the y-coordinate) by 1 unit.
Thus, if the coordinates of B are (-8, -2), the coordinates of A would be:
A = B + (3, 1)
A = (-8 + 3, -2 + 1)
A = (-5, -1)
Therefore, the pre-image point A has coordinates A(-5, -1).