Editing Affine transformation (section)

=== Properties preserved ===
An affine transformation preserves:
# [[collinearity]] between points: three or more points which lie on the same line (called collinear points) continue to be collinear after the transformation.
# [[Parallel (geometry)|parallelism]]: two or more lines which are parallel, continue to be parallel after the transformation.
# [[Convex set|convexity]] of sets: a convex set continues to be convex after the transformation. Moreover, the [[extreme point]]s of the original set are mapped to the extreme points of the transformed set.<ref name=res>{{cite web|last1=Reinhard Schultz|title=Affine transformations and convexity|url=http://math.ucr.edu/~res/math145A-2014/affine+convex.pdf|access-date=27 February 2017}}</ref>
# ratios of lengths of parallel line segments: for distinct parallel segments defined by points <math>p_1</math> and <math>p_2</math>, <math>p_3</math> and <math>p_4</math>, the ratio of <math>\overrightarrow{p_1p_2}</math> and <math>\overrightarrow{p_3p_4}</math> is the same as that of <math>\overrightarrow{f(p_1)f(p_2)}</math> and <math>\overrightarrow{f(p_3)f(p_4)}</math>.
# [[Barycentric_coordinate_system|barycenters]] of weighted collections of points.