This is a variation on our original task. It again uses the fact that a rotation is equivalent to two reflections about lines through the centre of rotation. It also uses the fact that a translation is equivalent to two reflections in lines at right angles to the translation, whose distance apart is half the distance of the translation.

If we rotate mirror lines m and n clockwise through 45˚ about A and move p and q one unit to the left, then we have not changed the overall effect of the four reflections, but the green and mauve lines coincide and so can be ignored.

We are left with two reflections, in the blue and brown lines in their new positions - what is the angle between them, and where do they intersect?

the end
a high-res pdf file of this new GEOaa-zz task