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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.