# 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. I've never heard of this crazy idea of an inverse, you might say. But you are mistaken! The inverse of multiplication is division, the inverse of addition is subtraction. You've been using function inverses every time you solve equations!

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