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Rotations about any point

Remember that a point and its image are always the same distance from the centre of rotation.


Describe the rotation which moves ABCD to A'B'C'D' in this diagram.

image: a graph with two squares plotted the first: A (1,1), B (1,4), C (3,4), D (3,1). The second A' (2, minus 2), D' (2, minus 4), B' (5, minus 2), C' (5, minus 4)

The centre of rotation is (0, -1).

We can see that A is the same distance from (0, -1) as A'.

D is the same distance from (0, -1) as D'.

The angle of rotation is 90° clockwise.

It is possible to use constructions to find the centre of rotation, but this can be time-consuming and complicated. Try to find the centre by observation, but remember that each point and its image must be the same distance from the centre of rotation.

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