If a dilation) (or scaling) is given, it is assumed that its center and a factor are given, so we can construct an image of any point.
If center of dilation is point O and factor is f≠0, any given point A is transformed by a dilation into point A' such that
(a) points O, A and A' are on the same line;
(b) if f>0, points A and A' are on the same side from center O; if f<0, point O is in between A and A';
(c) Lengths of segments OA' and OA relate to each other at factor |f|, that is |OA'|/|OA|=|f|
If these two parameters, the center and the factor, are not known, something must be given to determine them.
If a center O is given, to determine a factor we need points A and its image (the result of scaling) A'.
Then, knowing mutual position of points O, A and A' and lengths of segments OA and OA', we can determine a factor, its sign based on position of given points and its absolute value as the ratio of the lengths of segments OA' and OA.
If even a center is not given, we need two pairs of points: sources A and B and their images A' and B'.
Then we determine the center as an intersection of lines A A' and BB' and then follow the procedure above since a center is known now.
