How do we do compositions of transformations?

              How do we do compositions of transformations?

A composition of a transformation is when you have two or more transformations in order to a form a new transformation. When given this transformation you are suppose to do the second transformation FIRST, then followed by the first transformation SECOND.

For example if you were given r x-axis (followed by a open circle) T(3,4): You are suppose to do T(3,4) as your first transformation followed by the reflection over the x-axis.

Step 1: 

If you were given the coordinates (6,-7) and the composition, y=x (open circle) T(2,-8).

First you would do T(2,-8) --> (x+2) (y-8) --> then you would substitute the x and the y for your original coordinates   --> (6+2) (-7-8) --> (8,-15) 

Step 2:

Now once you have finished the translation, you now do y=x.

y=x is just (x,y) --> (y,x)

            (8,-15) --> (-15,8)

You have just completed a composition of a transformation!!