Composition of transformations

Aim: How do we identify composition of transformations?
 Answer:

Composition of Transformations:

    When two or more transformations are combined or joined to together in order to form a new transformation the result is known as a composition of transformations.

Example:



                                                                                                                         
Example Question and answer on composition of transformations:
Question: A triangle has vertices A(3,2), B(4,1) and C(4,3).  What are the coordinates of point B under a glide reflection,
?
Work: 
-We first start with the transformation shown on the right.

x=0 and (4,1) = (4,-1) - this is due to the fact that the original coordinates for the original point reflects from the first quadrant to the second quadrant causing the y value to become negative as shown above.


- Then we begin with the transformation on the left of the equation.

(4,-1)+(0,1)=(4,0)
Answer: the coordinates of point B under a glide reflection or B' is (4,0)

Try it yourself!:

Given triangle ABC: A(1,4), B(3,7), C(5,1) Graph and label the following composition:

Answer


                                                                                                        Answer: A'(-4,-6),B'(-2,-9),C'(0,-3)



  
Go Even Further(Critical Thinking):

                                        

Write a rule for the composition of a dilation of scale factor 3 following a translation of 2 units to the right.

Choose: A)
B)
C)
D)

                                                                 
                                                                                                                               Answer:A

To practice more on Composition of transformations visit: http://www.regentsprep.org/Regents/math/geometry/GT6/PracGlide.htm