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

.

Explanation:

Answer 2

for the element to be congruent only rotations, reflections or translations are allowed to be applied
1)
(x, y) → (x, –y)=reflection
(x, y) → (x + 5, y)=translation
(x, y) → (–x, y)=reflection
->is congruent
2)
(x, y) → (x + 1, y)=translation
(x, y) → (–x, –y)=reflection
(x, y) → (2x, y)=scaling->can't be congruent
3)
(x, y) → (0.5x, 0.5y)=scaling->can't be congruent
(x, y) → (x, –y)
(x, y) → (x, y + 8)
4)
(x, y) → (x – 4, y)=translation
(x, y) → (x, y + 3)=translation
(x, y) → (3x, 3y)=scaling->can't be congruent

so 1) is the only series of transformations with a congruent solution