1. The problem involves understanding the coordinates transformation given by the point $(x+9, y-2)$. 2. This represents a translation of any point $(x,y)$ in the Cartesian plane by shifting it 9 units to the right (adding 9 to the x-coordinate) and 2 units down (subtracting 2 from the y-coordinate). 3. The formula for translation is: $$ (x, y) \to (x + h, y + k) $$ where $h$ is the horizontal shift and $k$ is the vertical shift. 4. In this case, $h = 9$ and $k = -2$. 5. To find the new coordinates of any point after translation, simply add 9 to the original x-coordinate and subtract 2 from the original y-coordinate. 6. For example, if the original point is $(7, 5)$, the translated point is: $$ (7 + 9, 5 - 2) = (16, 3) $$ 7. Similarly, for the point $(1, -1)$, the translated point is: $$ (1 + 9, -1 - 2) = (10, -3) $$ This translation moves all points 9 units right and 2 units down on the Cartesian plane.