Answer:
The coordinates of the image is;
[tex]\begin{gathered} A^{\prime}=(2,1) \\ B^{\prime}=(4,1) \\ C^{\prime}=(4,4) \end{gathered}[/tex]
The image is graphed below;
Explanation:
We want to find and draw the reflection of y = -x;
with rule;
[tex](x,y)\rightarrow(-y,-x)[/tex]
Firstly, let us write out the coordinates of the preimage points;
[tex]\begin{gathered} A=(-1,-2) \\ B=(-1,-4) \\ C=(-4,-4) \end{gathered}[/tex]
Applying the reflection rule above;
[tex]\begin{gathered} (x,y)\rightarrow(-y,-x) \\ A(-1,-2)\rightarrow A^{\prime}(2,1) \\ B(-1,-4)\rightarrow B^{\prime}(4,1) \\ C(-4,-4)\rightarrow C^{\prime}(4,4) \end{gathered}[/tex]
Therefore, the coordinates of the image is;
[tex]\begin{gathered} A^{\prime}=(2,1) \\ B^{\prime}=(4,1) \\ C^{\prime}=(4,4) \end{gathered}[/tex]
The image is graphed below;
