The reflection of the polygon with vertices A(-2, -3), B(-2, 0), C(0, 1) in the line y=-x results in a new polygon with vertices A' (3, 2), B' (0, 2), and C' (-1, 0).
Finding the Image of A(-2, -3):
The reflection in the line y=-x involves swapping the x and y coordinates.
For A(-2, -3), the new coordinates A' are ( -(-3), -(-2) ), which simplifies to (3, 2).
Finding the Image of B(-2, 0):
Applying the reflection to B(-2, 0), we get B' = (0, -2) by swapping the x and y coordinates.
Finding the Image of C(0, 1):
For C(0, 1), the reflection results in C' = (-1, 0).
Therefore, the image of the given polygon after reflection in the line y=-x is a new polygon with vertices A' (3, 2), B' (0, -2), and C' (-1, 0).