Rotations

We will only consider rotations about the origin of multiples of 90^o.

Example 5:  Give a coordinate rule for a rotation about the origin of 90^o (counterclockwise).

Solution:  Such a rotation is equivalent to reflections in two lines that intersect at the origin and are 45^o apart.  We could use the x-axis as the first line and the line y = x as the second.  The composite of these reflections is:

(x, y) --> (x, –y) --> (–y, x)

That is, a rotation about the origin of 90^o has the coordinate rule:  (x, y) --> (–y, x)

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