Answer: Figure and its image are not the same.
Explanation:
To determine if the figure and its image are congruent, we need to determine if the image is the result of a combination of translations, reflections, and/or rotations of the original figure without any changes to size or shape.
Let's first consider the effect of the transformation (x, y) → (–x + 1, y + 1) on the x-coordinate. The transformation involves negating the x-value and then adding 1. This results in a reflection of the point across the y-axis followed by a translation to the right by 1 unit. This transformation is not a translation, rotation, or a combination of translations and rotations, so we can say that the image is not obtained by a sequence of rigid motions.
Therefore, we can conclude that the figure and its image are not congruent. The transformation changes the location of the figure and its shape, which means that the figure and its image are not the same.