Suppose that l,m,k,t differnt lines (Like this illustration)
Describe accurately this composition:
$S_k\circ\ S_t\circ\ S_m\circ\ S_l$
Well, composition of isometry is a group and i know that composition of two different reflections is a rotation. meaning, $S_k\circ\ S_t$ is rotation in 180°. same for $S_m\circ\ S_l$.
so $R\circ\ R$? what is the meaning of this composition?
Additionally i know that composition of 3 reflections is glide reflection, so $S_t\circ\ S_m\circ\ S_l$ is glide reflection. Let it be T.
Now i have $S_k\circ\ T$. Again, what is the meaning?
hope everything is clear. thanks.
The composition of two reflections is a rotation, and the composition of two rotations is again a rotation. So you get a rotation. (This reasoning uses the fact that $(A\circ B)\circ (C\circ D) = A\circ B\circ C\circ D$)
In two dimensions, to figure out the angle you just have to check one vector.