1. **Problem statement:** Draw the image of triangle A after (i) a reflection in the line $y = -x$ and (ii) a translation by the vector $(-2, -9)$. 2. **Reflection in the line $y = -x$:** The rule for reflecting a point $(x, y)$ in the line $y = -x$ is to swap and negate the coordinates: $(x, y) \to (-y, -x)$. 3. **Vertices of triangle A:** Given approximately as $(1, 2)$, $(4, 2)$, and $(1, 7)$. 4. **Apply reflection to each vertex:** - $(1, 2) \to (-2, -1)$ - $(4, 2) \to (-2, -4)$ - $(1, 7) \to (-7, -1)$ 5. **Translation by vector $(-2, -9)$:** The rule for translation is to add the vector components to each vertex: $(x, y) \to (x - 2, y - 9)$. 6. **Apply translation to original vertices of triangle A:** - $(1, 2) \to (1 - 2, 2 - 9) = (-1, -7)$ - $(4, 2) \to (4 - 2, 2 - 9) = (2, -7)$ - $(1, 7) \to (1 - 2, 7 - 9) = (-1, -2)$ **Final answers:** - Reflected triangle vertices: $(-2, -1)$, $(-2, -4)$, $(-7, -1)$ - Translated triangle vertices: $(-1, -7)$, $(2, -7)$, $(-1, -2)$