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)

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

The surface area would be 576 because you multiply all the numbers then multiply that number by 6