Let us start by writing the coordinates of the parent image and transformed image
Coordinates of the parent image
[tex]\begin{gathered} A\rightarrow(-1,-1) \\ B\rightarrow(-4,0) \\ C\rightarrow(2,2) \end{gathered}[/tex]
Coordinates of the transformed image
[tex]\begin{gathered} A^{\prime}\rightarrow(1,-1) \\ B^{\prime}\rightarrow(4,0) \\ C^{\prime}\rightarrow(-2,2) \end{gathered}[/tex]
From the coordinates of the parent image and the transformed image collated above, we can conclude that the x-axis of the parent image was multiplied by (-) negative sign while the y-values remaining constant.
The mathematical representation is,
[tex](-x,y)[/tex]
Checking for confirmation
[tex]\begin{gathered} A\rightarrow(-(-1),-1)\rightarrow(1,-1)\rightarrow A^{\prime} \\ B\rightarrow(-(-4),0)\rightarrow(4,0)\rightarrow B^{\prime} \\ C\rightarrow(-(2),2)\rightarrow(-2,2)\rightarrow C^{\prime} \end{gathered}[/tex]
Therefore, the rule that satisfies the transformation is a reflection across the y-axis.
The correct option is Option 5.
