The given composition of isometries represents a glide reflection.
R_(y=-2)∘ T_(<-4,0>)
Reflection across y=-2
Translation 4 units left
To complete a glide reflection, we first perform the translation and then the reflection. Let's begin by plotting the given points and tracing the lines to graph △ TAM.
Translation
To move △ TAM four units left, we have to subtract 4 from each x-coordinate.
T_(<-4,0>)(x,y) → (x-4,y)
Let's do this.
Reflection
To complete the reflection, we have to move all of the vertices of △ T'A'M' to the opposite side of the line y=2 in a way such that the distance from the vertices to the line remains the same.
Final Glide Reflection
The final glide reflection is the combined translation and reflection.
