Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by(adsbygoogle = window.adsbygoogle || []).push({});

x1=x+a(x-y)

Given that a is positive number, how can it be shown that the distance x1 to y is larger than distance x to y. I'm mainly interested in a vector interpretation of the above update rule. In that sense, can (x-y) in the above rule be interpreted as

direction (force) from point y to point x? Similar interpretation is welcome.

Given negative a, the update is x1=x+a(y-x), so now the above intuition of a force is direction from point x to point y.

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# Understanding displacements of points by interpreting directions

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