How do we do compositions of transformations?

Composition of Transformations

When two or more transformations are combined to form a new transformation, the result is called a composition of transformations 

                     Do second → rx-axis º T(3,4) ← Do first

Example 1: Find the coordinates of the image of A(2,4) under the transformation ry-axis º T(3,-5).

Answer: A(2,4)→A'(5,-1)→A''(-5,-1)

Example 2: Find the image of point A(3,-2) under the composition of translation T(2,1) º T(-6,-4).

Answer: A(3,-2)→A'(-3,-6)→A''(-1,-5)