Motion invariance

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In geometry , a property is called motion-invariant if it does not change through the application of a movement (i.e. a congruence mapping ). For example, the distance between two points is invariant to movement, since the distance between the image points P 'and Q' and the distance between the original points P and Q after any movement.

Motion-invariant properties of a plane curve are, for example, its length and its curvature . In contrast, the slope and the position of the extremes are not motion-invariant .

In analytic geometry , motion invariance can also be understood as being independent of the choice of the coordinate system .