19. Which of the following is the composition rewritten as a single translation? Translation: \( (x, y) \rightarrow(x+9, y-8) \) Translation: \( (x, y) \rightarrow(x-3, y-4) \) (A) \( (x, y) \rightarrow(x+6, y-12) \) (B) \( (x, y) \rightarrow(x+12, y-4) \) (C) \( (x, y) \rightarrow(x+6, y-4) \) (D) \( (x, y) \rightarrow(x+12, y-12) \)

To find the composition of the two translations, we need to apply them one after the other. Here’s how we do it: 1. Start with the point \((x, y)\). 2. Apply the first translation: \((x, y) \rightarrow (x + 9, y - 8)\). 3. The result is now \((x + 9, y - 8)\). 4. Apply the second translation to this result: \((x + 9, y - 8) \rightarrow (x + 9 - 3, y - 8 - 4)\). 5. Simplifying that gives us \((x + 6, y - 12)\). That’s looking to be perfect for option (A): \( (x, y) \rightarrow (x + 6, y - 12) \). So the answer is (A) \( (x, y) \rightarrow (x + 6, y - 12) \).