First, let's write the vertices of the quadrilateral ABCD.
According to the given image, the vertices are A(1,1), B(2,3), C(4,3), D(5,1).
The first transformation a reflection across the y-axis means we have to multiply each x-coordinate by -1 to change its sign.
[tex]\begin{gathered} A(1,1)\rightarrow A^{\prime}(-1,1) \\ B(2,3)\rightarrow B^{\prime}(-2,3) \\ C(4,3)\rightarrow C^{\prime}(-4,3) \\ D(5,1)\rightarrow D^{\prime}(-5,1) \end{gathered}[/tex]The second transformation a translation 2 units down means we have to subtract 2 units from each y-coordinate.
[tex]\begin{gathered} A^{\prime}(-1,1)\rightarrow A^{\doubleprime}(-1,1-2)\rightarrow A^{\doubleprime}(-1,-1) \\ B^{\prime}(-2,3)\rightarrow B^{\doubleprime}(-2,3-2)\rightarrow B^{\doubleprime}(-2,1) \\ C^{\prime}(-4,3)\rightarrow C^{\doubleprime}(-4,3-2)\rightarrow C^{\doubleprime}(-4,1) \\ D^{\prime}(-5,1)\rightarrow D^{\doubleprime}(-5,1-2)\rightarrow D^{\doubleprime}(-5,-1) \end{gathered}[/tex]Once we made both transformations, we can draw the quadrilateral.
