Question

Find a single translation that has the same effect as each composition of translations.

(x, y) to (x + 6, y + 9) followed by (x, y) to (x - 4, y - 5)

Answer 1

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).