Which transformation will result in an image that is congruent to its pre-image?

Question

Which transformation will result in an image that is congruent to its pre-image?

1.  (x, y) → (−x, −4y) 
2. (x, y) → (4x, y − 4) 
3. (x, y) → (−4x, y)
4. (x, y) → (−x, −y)

Answer 1

only 4

(x,y) to (-x,-y)

it's a reflection around both axes,

reflect over y axis gives (-x,y)

then reflect over x axis to get (-x,-y)

or

it's a rotation, either counterclockwise or clockwise of 180 degrees or pi radians, about the origin

Answer 2

(x, y) → (-x, -y) is a rotation of 180° centered at the origin