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TWO-PAIRS-2

In this movie we rotate the first pair of mirror lines such that the green line goes through points A and U (note that we don't change the point of intersection or the 30˚ angle between the lines). We then rotate the second pair such that the mauve line also goes through A and U (again, we don't change the point of intersection or the 30˚ angle between the lines).

This means that the four reflections are now equivalent to two - in the blue and then the brown line (in their new positions).
• What is the angle between these two lines and where do they meet?
• What single transformation is this equivalent to?

You might want to explore the situation further using the JAVA-2 worksheet, which allows you
• to move the grey object flag freely (which might make the centre of rotation more apparent)
• to rotate both pairs of mirror lines (so as to cancel out a pair of mirrors)
• to move the points of intersection (and thus make the task simpler or more challenging).

On the final page, we present another task where two transformations (a rotation and a translation this time) are treated as four reflections, which in turn are reduced to two reflections, which in turn are interpreted as a rotation whose centre and angle of rotation we can determine.