What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?

Question

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?

1.  Reflected over the x-axis and rotated 180° 
2. Reflected over the y-axis and rotated 180°
3.  Reflected over the x-axis and rotated 90° counterclockwise 
4. Reflected over the y-axis and rotated 90° counterclockwise

Answer 1

(2) is the correct answer choice.

Reflecting over the y-axis (x,y) --> (-x,y).

Rotating 180 degrees (around the origin):

(x,y) --> (-x,-y).

Applying these both in the above order:

(x,y) --> (-x,y) --> (x,-y)

which is the same as a reflection across the x-axis.

And this is clearly a reflection over the x-axis.