Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by 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.