Answer:
The coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Explanation:
From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.
Which has a rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Applying the rule to the given points. we have;
[tex]\begin{gathered} A(-5,-3)\rightarrow A^{\prime}(3,-5) \\ B(-4,0)\rightarrow B^{\prime}(0,-4) \\ C(-2,0)\rightarrow C^{\prime}(0,-2) \\ D(0,-3)\rightarrow D^{\prime}(3,0) \end{gathered}[/tex]Then the produced image was then reflected over the x-axis;
Reflection across the x-axis have the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule to the resulting image;
[tex]\begin{gathered} A^{\prime}(3,-5)\rightarrow A^{\prime^{}}^{\prime}(3,5) \\ B^{\prime}(0,-4)\rightarrow B^{\prime}^{\prime}(0,4) \\ C^{\prime}(0,-2)\rightarrow C^{\prime^{}}^{\prime}(0,2) \\ D^{\prime}(3,0)\rightarrow D^{\prime}^{\prime}(3,0) \end{gathered}[/tex]Therefore, the coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]