Question

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.

Answer 1

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.

Answer 2

option: D.

Explanation:

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.)