Final answer:
The coordinates of point A" after the two given translations (x, y) → (x-2, y+1) and (x, y) → (x-6, y-4) are (x-8, y-3).
Step-by-step explanation:
To find the coordinates of point A" after the triangle ABC is translated twice, we need to apply the given transformations to the original coordinates of point A.
Assuming point A has coordinates (x, y), the first translation, (x, y) → (x-2, y+1), moves point A 2 units to the left and 1 unit up.
Therefore, the new coordinates of point A after the first translation are (x-2, y+1).
The second translation, (x, y) → (x-6, y-4), is then applied to the result of the first translation.
Thus, the coordinates become: (x-2-6, y+1-4), which simplifies to (x-8, y-3).
These are the final coordinates of point A" after both translations.
Hence, if we start with point A at coordinates (x, y), after the two translations, point A" will end up at coordinates (x-8, y-3).