1. **State the problem:** We need to find the image of a triangle after reflecting it across the y-axis and then translating it by the vector $v=(-1,0)$. The original triangle has vertices approximately at $(-7,-1)$, $(-4,2)$, and $(-2,-1)$. 2. **Reflection across the y-axis:** Reflecting a point $(x,y)$ across the y-axis changes its x-coordinate to $-x$ while keeping the y-coordinate the same. The formula is: $$ (x,y) \to (-x,y) $$ 3. **Apply reflection to each vertex:** - $(-7,-1) \to (7,-1)$ - $(-4,2) \to (4,2)$ - $(-2,-1) \to (2,-1)$ 4. **Translation by vector $v=(-1,0)$:** Translating a point $(x,y)$ by $(-1,0)$ means subtracting 1 from the x-coordinate and adding 0 to the y-coordinate: $$ (x,y) \to (x-1,y) $$ 5. **Apply translation to reflected vertices:** - $(7,-1) \to (7-1,-1) = (6,-1)$ - $(4,2) \to (4-1,2) = (3,2)$ - $(2,-1) \to (2-1,-1) = (1,-1)$ 6. **Final image vertices:** The triangle after reflection and translation has vertices at $(6,-1)$, $(3,2)$, and $(1,-1)$. This completes the transformation.