The given vertices are A(1,4), B(3,-2), and C(4,2).
The reflection over the x-axis is expressed as
[tex](x,y)\rightarrow(x,-y)[/tex]This means we have to multiple each y-coordinate with -1. Let's do it!
[tex]\begin{gathered} A(1,4)\rightarrow A^{\prime}(1,-4) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,2)\rightarrow C^{\prime}(4,-2) \end{gathered}[/tex]