Afigure is translated by (x-5,y+7), then by (x+5,y-7). without graphing, what is the final position of the figure?

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.