Final answer:
The single translation that has the same effect as the given sequence of translations is from (x, y) to (x + 2, y + 4), which is determined by adding the x and y components of the original translations.
Step-by-step explanation:
The student is asking how to find a single translation that has the same effect as two consecutive translations on a point in the plane. The first translation moves a point (x, y) to (x + 6, y + 9), and the second translation moves a point (x, y) to (x - 4, y - 5).
To combine these translations into a single translation, you simply add the respective components of the translations. For the x-coordinates, you combine 6 and -4 to get 2, and for the y-coordinates, you combine 9 and -5 to get 4. Therefore, the single translation that combines the effects of the two given translations is (x, y) to (x + 2, y + 4).