Our second one says to add 1 to our x so a double prime, if I add 1 to 2 that's going to be 3 and if I add 3 to my y we're going to be at 0 because -3+3 is 0 so a double prime is that 1, 2, 3 0 so I'm going to write a double prime right there. So let's say point a is right here and that is at 1, 2, 3, 4 up 1, 2, 3, 4 so point a is going to be at 4, 4 so when I perform my first translation which I know because we're adding and subtracting from y and x, x-2 well 2-4 is going, excuse me 4-2 is 2 so we know that our a prime which I'm going to write right here, a prime will be at 2 and from 4 I need to subtract 7 so that's going to be at -3 so I'm going to go over 2 and then down 1, 2, 3 and that will be my a prime we performed our first translation. So let's look at what translating point a according to these two order pair rules would actually be equivalent to, so our first one we have xy maps onto x-2 and y-7, so to get an idea let's just pick a point a anywhere on our order plane. When you put 2 or more of those together what you have is the composition of transformations, so basically what you're saying is you could translate something and then reflect it and that would a composition of transformations. We said there are 3 types of isometries, translations, reflections and rotations.

Rotation rules geometry