The coordinates of the image of the triangle after the translation are A'(-3, 0), B'(-1, 4), and C'(2, 2).
To translate the triangle 1 unit left and 2 units up, we need to subtract 1 from the x-coordinates of each vertex and add 2 to the y-coordinates of each vertex.
The original vertices of the triangle are A(-2, -2), B(0, 2), and C(3, 0).
After the translation, the new coordinates of the vertices are:
A'(-2 - 1, -2 + 2) = (-3, 0)
B'(0 - 1, 2 + 2) = (-1, 4)
C'(3 - 1, 0 + 2) = (2, 2)
Therefore, the coordinates of the image of the triangle after the translation are A'(-3, 0), B'(-1, 4), and C'(2, 2).