1. **Problem statement:** We have triangle $\triangle ABC$ with vertices $A(1,-3)$, $B(-2,-2)$, and $C(-1,0)$. The triangle is translated by $+5$ units in the x-direction and $-4$ units in the y-direction. We need to find the coordinates of the new triangle after this translation. 2. **Translation formula:** When a point $(x,y)$ is translated by $h$ units in the x-direction and $k$ units in the y-direction, the new coordinates $(x',y')$ are given by: $$ (x', y') = (x + h, y + k) $$ 3. **Apply the translation to each vertex:** - For $A(1,-3)$: $$ A' = (1 + 5, -3 - 4) = (6, -7) $$ - For $B(-2,-2)$: $$ B' = (-2 + 5, -2 - 4) = (3, -6) $$ - For $C(-1,0)$: $$ C' = (-1 + 5, 0 - 4) = (4, -4) $$ 4. **Final answer:** The coordinates of the new triangle $\triangle A'B'C'$ are: $$ A'(6, -7), \quad B'(3, -6), \quad C'(4, -4) $$