What set of transformations could be applied to rectangle abcd to create a'b'c'd'?

reflected over the x-axis and rotated 180°
reflected over the y-axis and rotated 180°
reflected over the x-axis and rotated 90° counterclockwise
reflected over the y-axis and rotated 90° counterclockwise

Vertices of the given rectangle ABCD is

A(-4,2)

B(-4,1)

C(-1,1)

D(-1,2).

Vertices of transformed rectangle A'B'C'D' are

A'(2,-4)

B'(1,-4)

C'(1,-1)

D'(2,-1)

Let us observe transformations

A(-4,2) --> A'(2,-4)

B(-4,1) --> B'(1,-4)

C(-1,1) --> C'(1,-1)

D(-1,2) --> D'(2,-1)

Form the reflected coordinates, we can clearly see that only x and y coordinates of each point are switched.

If original rectangle has vertices in form (h,k).

First if we reflect over x-axis, the coordinate(h,k) would become (h,-k).

Now if we rotate it rotated 90° counterclockwise, the x and y-coordinates switches and x-coordinate would be multiply by -1.

So, after rotated 90° counterclockwise (h,-k), we get (k,h)

So, finally the x and y-cordinates values get switched.

Therefore, correct option is third option, that is

Reflected over the x-axis and rotated 90° counterclockwise.

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