Homothety, with centre O (a point) and ratio k (a number belonging to R\{0}) , is a geometric transformation where each transformed point Q' corresponds to an initial Q.

Q' belongs to the straight line passing through O and Q;
if k>0, then Q' is located on the same side as Q in relation to O;
if k<0, then Q' is located on the opposite side of Q in relation to O;
the ratio Q'O/QO is equal to |k|.

In the example above I used the Y-axis formula, y=mx+q, to enable the generation of straight lines on a bidimensional plane.