1. The problem asks to find the new coordinates of triangles after applying given translations. 2. Translation means moving every point of a shape by the same amount in a given direction. 3. The formula for translation is: $$\text{New point} = \text{Original point} + \text{Translation vector}$$ 4. For the first translation vector $$\begin{pmatrix}-4 \\ -1\end{pmatrix}$$, each vertex of triangle ABC moves left by 4 units and down by 1 unit. 5. For the second translation vector $$\begin{pmatrix}-2 \\ 4\end{pmatrix}$$, each vertex of triangle EFG moves left by 2 units and up by 4 units. 6. Suppose the original coordinates of triangle ABC are $$A(x_A,y_A), B(x_B,y_B), C(x_C,y_C)$$. 7. Then the new coordinates after translation are: $$A' = (x_A - 4, y_A - 1)$$ $$B' = (x_B - 4, y_B - 1)$$ $$C' = (x_C - 4, y_C - 1)$$ 8. Similarly, for triangle EFG with original points $$E(x_E,y_E), F(x_F,y_F), G(x_G,y_G)$$, the new points are: $$E' = (x_E - 2, y_E + 4)$$ $$F' = (x_F - 2, y_F + 4)$$ $$G' = (x_G - 2, y_G + 4)$$ 9. Without the original coordinates, the exact numeric answers cannot be given, but the method above shows how to find the new points after translation. 10. To find the exact new coordinates, subtract or add the translation vector components to each original vertex coordinate accordingly.