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.
