Answer:
" a glide reflection IS commutative. Therefore, the line reflection and translation can be done in any order."
Step-by-step explanation:
Transformations can be written as operators that act on functions or shapes.
For example, we can define the horizontal translation operator as:
T(k)
And if we apply this to a function, we get:
T(k)[ f(x) ] = f(x - k)
Now, the operators are not necessarily commutative.
This means that if we have two operators:
K and L
is not the same:
K[ L[ f(x) ]]
than:
L[ K[ f(x) ]]
An example of this can be a reflection across the y-axis and a horizontal translation, that composition is non-commutative.
Now, let's go to our case.
A glide reflection is commutative, so we can perform the transformations in any order, then the statement is:
" a glide reflection IS commutative. Therefore, the line reflection and translation can be done in any order."
