# Exploring Translations 3

## Question 3

a) Translate the polygon so that point A is at the origin (0,0). How far did the polygon move from its **original position**? How would you write this change in position so that someone could reproduce it without a picture?
b) Translate the polygon so that point A is at the point (1,3). How far did the polygon move from **the last ** position? How would you write this change in position so that someone could reproduce it without a picture?

Did you notice that the shifts in question 3 were opposites? Shift 1 took the pre-image (brown) and translated it (pink). In shift 2, the pink shape was the pre-image, and it was translated back to where the brown shape was. It turns out that translations are actually functions that take a point as input and then output another point (possibly the same point).
In math language a function that "undoes" another function is called an inverse. Transformation functions have inverses, and you just found one. Remember that functions are inverses if the inputs/outputs become switched. For example, (2,5) would be (5,2)

*Check your answers, then go on to Exploring Translations 4.*