Triangle A'B'C' with coordinates of A' (-6,2)

(A), (B) and (E).

Step-by-step explanation: Given that ΔA’B’C’ with coordinates of A(-6,2),B’(-4,2), and C’(-6,-2) is the image of ΔABC after a translation of (x-3,y+2). We are to find the possible coordinates for the original vertices of ΔABC.

For vertex A, we have

So, the coordinates of vertex A are (-3, 0).

For vertex B, we have

So, the coordinates of vertex B are (-1, 0).

For vertex C, we have

So, the coordinates of vertex C are (-3, -4).

step-by-step explanation: