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Teacher Notes

CONCEPT 2 -Specify a sequence of transformations that will carry a given figure onto another.

COMPOSITE FUNCTIONS

Composite function is the term for when a sequence of transformation take place.  So if we reflection point A over the x axis we get A’ and then if we rotate A’ 90° about the origin we get A’’.  The first thing to notice is that as we perform transformation in a succession we continue to label with the primes to show who is the pre-image of who.  A is the pre-image of A’, A’ is the pre-image of A’’, A’’ is the pre-image of A’’’, and so on.

 TEACHER NOTE -- These connects nicely to composite functions. The order that things are done definately matters. Composite functions and transformations are NOT COMMUTATIVE!!!

DOES THE ORDER WE DO THEM IN MATTER?    YES!!!!!

DOUBLE REFLECTIONS OVER PARALLEL LINES

 Analysis of ΔABC &ΔA’’B’’C’’ Orientation is the same. All points moved a fixed distance. All points moved a fixed direction. Analysis of ΔABC &ΔA’’B’’C’’ Orientation is the same. All points moved a fixed distance. All points moved a fixed direction.

The translation is double the distance between the parallel lines.

 TEACHER NOTE -- The order determine the direction. The distance is fixed based on the distance between the lines but the direction depends on the order of the reflections and the their slopes.

Some students think that the location of pre-image determines the direction that it will go during the reflections.  IT HAS NOTHING TO DO WITH IT.  Double distance between the parallel lines determines the distance and the ORDER determines the DIRECTION.

DOUBLE REFLECTIONS OVER INTERSECTING LINES

 Analysis of ΔABC &ΔA’’B’’C’’ Orientation is the same. All points moved on an arc All points the same distance from the center of rotation Analysis of ΔABC &ΔA’’B’’C’’ Orientation is the same. All points moved on an arc All points the same distance from the center of rotation

A double reflection is a ROTATION. The rotation is double the angle formed between the intersecting lines.

Some students think that the location of pre-image determines the direction that it will go during the reflections.  IT HAS NOTHING TO DO WITH IT.  The angle direction will be determined by the order of the reflections.