For ΔABC, which transformation composition is COMMUTATIVE?
A) rotate 30 degrees and then translate 2 units down
B) translate 5 units to the right and rotate 90 degrees
C) reflect across the y-axis and then rotate 90 degree Eliminate
D) reflect across the y-axis and then reflect across the x-axis.
Commutative transformation is type of transformation in which the order of operations doesn't affect the result of transformation. The only commutative transformation is D.
We are asked which transformation composition is COMMUTATIVE i.e. we are asked to find that the resultant figure is independent of the operations applied to it in any order.
Also we know that translation and rotation together are not commutative hence, A and B options are incorrect.
Also rotation and reflection applied to a figure are not commutative.
But a pair of reflection applied to a figure will be commutative
Hence, option: D is correct. (reflect across the y-axis and then reflect across the x-axis.)
