Another (maybe more intuitive) way to look at affine transformations is to define them as transformations which preserve points, lines and planes. Parallel lines must stay parallel, meaning you can have transformations that turn squares into parallelograms, but not into trapezoids.

Another (maybe more intuitive) way to look at affine transformations is to define them as transformations which preserve points, lines and planes. Parallel lines must stay parallel, meaning you can have transformations that turn squares into parallelograms, but not into trapezoids.