Individual Mirrors

Suppose our symmetry group for the strip has a reflection. Think about its mirror line. Can its mirror line be

Parallel to the x-axis?

If so, with what y-value? Remember, the symmetry has to take the strip $-1 \leq y \leq 1$ to itself.

Parallel to the y-axis?

With what x value?

Not parallel to one of the coordinate axes?

What happens to points near the intersection of the mirror line with the boundary lines $y=\pm 1$ of the strip.