Homothety
In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point  called the origin. The number  by which distances are multiplied is called the dilation factor or similitude ratio. Such a transformation is also called an enlargement.
Choose an origin or center and a real number (possibly negative). The homothety  maps any point  to a point  such that  (vectors here). In other words,  are aligned and the (algebraic) distance  is times the distance  . (Algebraic means here that sign matters; for instance if  then  , which means that is on the other side of .)
A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by , all surfaces by  , etc.
Referenced By
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