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The key to this task is to find a pair of mirror lines m' and n' that intersect at an angle of 30˚ through point A, and a pair p' and q' that intersect at an angle of 30˚ through point U, such that n' and p' cancel out. Point C will then be at the intersection of m' and q'.

Before pursuing this solution, we explore the geometric property underlying the task, namely that a rotation of r˚ about a point A is equivalent to reflections in two mirror lines that intersect at an angle of r˚/2 through the point A.

On the next two pages we demonstrate that a pair of reflections in mirror lines that intersect at 45˚ is equivalent to a 90˚ rotation about the point of intersection of the mirror lines. We show that this holds
• when we move the object [next page] and
• when we rotate the mirror lines (as long as the point of intersection and the angle between the lines does not change) [next but one page].

We then provide a worksheet [JAVA-1] where these variants can be explored more interactively.

After this, we explore what happens with two pairs of mirror lines, as in the given task.

FREE:
a high-res pdf file of this new GEOaa-zz task