Solution:
Given a graph with triangle ABC;
The coordinates of ABC are
[tex]\begin{gathered} A(-1,1) \\ B(1,4) \\ C(3,-2) \end{gathered}[/tex]
If the image is translated 5 units to the left, that means, subtracting 5 from the x coordinates of ABC
[tex]\begin{gathered} A(-1-5,1)\Rightarrow A(-6,1) \\ B(1-5,4)\Rightarrow B(-4,4) \\ C(3-5,-2)\Rightarrow(-2,-2) \end{gathered}[/tex]
Then, the image is translated 2 units down, i.e. subtracting 2 units from the y coordinates of the ABC
[tex]\begin{gathered} A(-6,1-2)\Rightarrow A(-6,-1) \\ B(-4,4-2)\Rightarrow B(-4,2) \\ C(-2,-2-2)\Rightarrow C(-2,-4) \end{gathered}[/tex]
The coordinates are
[tex]\begin{gathered} A(-6,-1) \\ B(-4,2) \\ C(-2,-4) \end{gathered}[/tex]
Hence, the figure is
