Question

Which series of transformations results in the image being congruent to the pre-image?

(x, y) → (–x, –y)
(x, y) → (0.8x, 0.8y)
(x, y) → (x, y + 5)

(x, y) → (x, –y)
(x, y) → (–x, y)
(x, y) → (x + 1, y – 1)

(x, y) → (x + 5, y + 5)
(x, y) → (x, –y)
(x, y) → (2x, y)

(x, y) → (3x, 3y)
(x, y) → (–x, y)
(x, y) → (x – 4, y)

Answer 1

images of transformation are congruent if they were translated, mirrored/flipped or rotated

1)
(x, y) → (–x, –y) mirrored
(x, y) → (0.8x, 0.8y) scale->not congruent
(x, y) → (x, y + 5)

2)
(x, y) → (x, –y) mirrored
(x, y) → (–x, y) mirrored
(x, y) → (x + 1, y – 1) translation
-> is congruent

3)
(x, y) → (x + 5, y + 5) translation
(x, y) → (x, –y) mirror
(x, y) → (2x, y) scale-> not congruent

4)
(x, y) → (3x, 3y) scale->not congruent
(x, y) → (–x, y)
(x, y) → (x – 4, y)

so the second series of transformations is the only one with a congruent after image