This worksheet allows you to see what a Euclidean motion defined by a formula looks like.
The transformations f and g are defined by f(x,y) = (fx(x,y),fy(x,y)), g(x,y) = (gx(x,y),gy(x,y)), and starting from the "original" bird, we draw f(bird) (which starts out as the rotation around the origin by angle theta) and g(bird) (which starts out as the reflection over the line through the origin forming an angle theta/2 with the x-axis).