In the given diagram we want to identify the transformation that maps â–³MNP onto â–³EDC.
We cannot map â–³MNP onto â–³EDC by moving â–³MNP and maintaining its orientation, so it is not a translation. Also, we can see that â–³EDC is not a rotation of â–³MNP. Therefore, the mapping can be a glide reflection or a reflection across the line x=- 0.5. Let's first see the glide reflection and then we will explain the reflection at the bottom.
Writing the Rule
A glide reflection is the composition of a translation and a reflection across a parallel line to the direction of translation. Let's perform a glide reflection on â–³MNP and see if we can map it onto â–³EDC.
We can see that the glide reflection that maps △MNP onto △EDC consists of a translation 9 units to the left, followed by a reflection in the line x=-5. This composition of transformations can be written as (T_(<-9,0>) ∘ R_(x=-5))(x,y).
Alternative Solution
Reflection
We can also see a line of symmetry between â–³MNP and â–³EDC. The reflection is across the line x=- 0.5. Let's see it!
Therefore, we can write a second rule for this transformation as a reflection across the line x=- 0.5.
