Which sequence of transformations produces a congruent figure?

note: each answer choice represents a sequence of two transformations.

(x+2, y)(−x, −2.5y)

(x+2, 2y)(x+1, y−4)

(−x, 3y)(x−2, y)

(−x, y)(x−4, y+2)

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)

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