Question

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

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

(x, y) → (x + 1, y)
(x, y) → (–x, –y)
(x, y) → (2x, y)

(x, y) → (0.5x, 0.5y)
(x, y) → (x, –y)
(x, y) → (x, y + 8)

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

Answer 1

"images of transformation are congurent if they were translates, mirrored/flipped or rotated

1) (x, y) → (x, –y) flipped

(x, y) → (x + 5, y) translated

(x, y) → (–x, y) flipped

->is congruent

2) (x, y) → (x + 1, y) translated

(x, y) → (–x, –y) flipped

(x, y) → (2x, y) scaled->not congruent

3) (x, y) → (0.5x, 0.5y) scaled-> not congurent

(x, y) → (x, –y)

(x, y) → (x, y + 8)

4) (x, y) → (x – 4, y) translated

(x, y) → (x, y + 3) translated

(x, y) → (3x, 3y) scaled->not congruent

so only the first series of transformations has congruent after image"

Explanation:

Answer 2

images of transformation are congurent if they were translates, mirrored/flipped or rotated
1)
(x, y) → (x, –y) flipped
(x, y) → (x + 5, y) translated
(x, y) → (–x, y) flipped
->is congruent
2)
(x, y) → (x + 1, y) translated
(x, y) → (–x, –y) flipped
(x, y) → (2x, y) scaled->not congruent
3)
(x, y) → (0.5x, 0.5y) scaled-> not congurent
(x, y) → (x, –y)
(x, y) → (x, y + 8)
4)
(x, y) → (x – 4, y) translated
(x, y) → (x, y + 3) translated
(x, y) → (3x, 3y) scaled->not congruent

so only the first series of transformations has congruent after image