The geometric transformations of the plane or space most commonly considered generally preserve collinearity: the images of three collinear points are themselves collinear. This is true of rotations and translations, but also of orthogonal projections onto a line or a plane.
These transformations also preserve ratios of lengths: if one of two line segments on the same line D is twice as long as the other, the same is true of their images on the line D’, the image of D.
The translation by vector preserves the collinearity of points A, B and C, as well as the relative position of B within the line segment [AC].
The artists’ contribution
---------------------
