Without graphing, the final position of the figure that is translated by
(x - 5, y + 7), and then by (x + 5, y -
7) ends
up in the same position it was, before the translations.
Let’s check this example:
Think of point (1, 1). The point is translated to (-4, 8); and then it is moved
back to point (1, 1). The x spot’s -5 and +5 cancel each other out and the same
can be said for the y’s.
To add, a geometric transformation that changes every point of a space by the same amount
in a given direction or a figure is called a translation.
