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

(x,y)---> (x+7,y-2) followed by
(x,y)---> (x-3,y+2).

(x,y) -> (x+7,y-2) -> ((x-3)+7,(y+2)-2) = (x+4,y)

confusion it is

To find a translation that has the same effect as the composition of translations (x,y) ---> (x+7,y-2) followed by (x,y) ---> (x-3,y+2), we can simply combine the translation vectors of the two translations.

The first translation (x,y) ---> (x+7,y-2) can be represented as a vector (7, -2).
The second translation (x,y) ---> (x-3,y+2) can be represented as a vector (-3, 2).

To combine the translation vectors, we add the corresponding components:
(7, -2) + (-3, 2) = (7-3, -2+2) = (4, 0).

Therefore, the translation that has the same effect as the composition of the given translations is:
(x, y) ---> (x+4, y).

To find a translation that has the same effect as the composition of translations given, we need to determine the resulting translation vector.

Let's denote the first translation as T1: (x,y) --> (x+7, y-2).
And the second translation as T2: (x,y) --> (x-3, y+2).

To find the resulting translation vector, we can analyze the effect of applying both translations consecutively.

If we start with a point (x, y) and apply the first translation T1, we get (x+7, y-2).
Now, if we apply the second translation T2 to this new point, we get (x+7-3, y-2+2), which simplifies to (x+4, y).

Hence, the overall effect of the composition of translations T1 followed by T2 is the translation (x,y) --> (x+4, y).

Therefore, we can conclude that the translation (x,y) --> (x+4, y) has the same effect as the composition of translations you provided.