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PAIR-2

In this movie, we again show the image of a grey flag in a blue mirror line and the image of this image in a green mirror line (the angle between the mirror lines is again 45˚).
However, this time the grey flag does not move. Instead the mirrors move, but in such a way that their point of intersection and the angle between the lines does not change. You might want to pause the movie to examine the reflections more closely. Students might notice that the first image moves but the second does not - Why? As such, the movie might seem rather uneventful - however, the very fact that the final image does not move is, in its way, quite dramatic!

Afte a while, the mirrors stop moving and the grey flag is then rotated through 90˚ about A, the point of intersection of the mirror lines.
It is worth asking students what they think has happened.
• Do they realise the rotation is through 90˚?
• Do they realise that the centre is at A ?

Again, it is important to stress that all we have here is a demonstration.
Can we prove that the two reflections are equivalent to a 90˚ rotation about A ?

You might want to explore the situation further using the JAVA-1 worksheet, which allows you to move the grey flag freely and to rotate the pair of mirror lines: moving the grey flag will cause both images to move, but, as in the movie, only the first image moves when the flags are rotated in unison about A.

On the next page we return to the original task and demonstrate that a reflection in m, then n, then p then q is equivalent to a rotation of 120˚.