Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.
The types of transformations that preserve congruency includes:
Rotation (Turn): Turns a figure around a fixed point.
Reflection (Flip): Flip of figure over a line where a mirror image is created.
Translation (Slide or glide): Sliding a shape to a new place without changing the figure.
However, dilation which enlarges of decreases the size of the image does not preserve congruency.v Dilation is denoted by multiplying a coordinate of the figure by a constant.
From the options, the first three options includes dilation as there is a coordinate that is multiplied by a constant.
(x+2, y)(−x, −2.5y)
(x+2, 2y)(x+1, y−4)
(−x, 3y)(x−2, y)
However, (-x, y) (x - 4, y + 2) preserves the congruency of the figure.
Hence, sequence of transformations that produces a congruent figure are (-x, y) and (x - 4, y + 2)