The reflection of △CDE with vertices C(-3, 6), D'(-1, 1), and E(3, 5), to its image △C'D'E' with vertices C'(6, -3), D'(1, -1), and E'(5, 3) is a congruent triangle.
The coordinates of the vertices of the original triangle and its image are as follows:
Vertex Original Triangle Coordinates Image Triangle Coordinates
C (-3, 6) (6, -3)
D (-1, 1) (1, -1)
E (3, 5) (5, 3)
As you can see, the coordinates of the vertices of the image triangle are simply the negatives of the coordinates of the corresponding vertices of the original triangle. This is because the reflection across the x-axis flips the triangle over the x-axis.
The lengths of the sides of the original triangle and its image are also equal. This is because the reflection across the x-axis preserves distances.
Therefore, the reflection of △CDE with vertices C(-3, 6), D'(-1, 1), and E(3, 5), to its image △C'D'E' with vertices C'(6, -3), D'(1, -1), and E'(5, 3) is a congruent triangle.