Graphing the triangle DEF, we have:
Now, translating the triangle 4 units right and 3 units down, we have the new vertices:
[tex]\begin{gathered} D(-5,2)\to D^{\prime}(-5+4,2-3)=D^{\prime}(-1,-1) \\ E(1,3)\to E^{\prime}(1+4,3-3)=E^{\prime}(5,0) \\ F(-4,-3)\to F^{\prime}(-4+4,-3-3)=F^{\prime}(0,-6) \end{gathered}[/tex]Graphing the triangle D'E'F', we have: