To find the image of the triangle, it is enough to determine the image of the vertices of the triangle after the given transformations.
Recall that a translation of 2 units to the right modifies the point (x,y) as follows:
[tex](x,y)\rightarrow(x+2,y).[/tex]
A translation of 3 units up, modifies the points (x,y) as follows:
[tex](x,y)\rightarrow(x,y+3).[/tex]
From the diagram, we get that the vertices of the triangle are:
[tex](4,0),(2,-4),\text{ and (-2,-2).}[/tex]
Therefore, their images after the given transformations are:
[tex]\begin{gathered} (4,0)\rightarrow(6,3), \\ (2,-4)\rightarrow(4,-1), \\ (-2,-2)\rightarrow(0,1)\text{.} \end{gathered}[/tex]
Answer:
