Transformations in the Coordinate Plane Transformations in the
coordinate plane are often represented by "coordinate rules" of
the form (x, y) --> (x', y'). This means a point whose
coordinates are (x, y) gets mapped to another point whose
coordinates are (x', y'). When possible, simple formulas are
given for x' and y' in terms of x and y. For example, (x, y) -->
(x + y, x – y) is a coordinate rule for some transformation and
maps the points (0, 0), (2, 0), (2, 5), and (0, 5) as follows:
(0, 0) --> (0, 0) (2, 0) --> (2, 2) (2, 5) --> (7, –3) (0, 5)
--> (5, –5) This transformation is not an isometry (it changes
the size of any figure) and the image of the blue rectangle with
those vertices is the red rectangle: Translations of geometric
figures in the coordinate plane can be determined by translating
the x- and y-coordinates of points. Horizontal and vertical
translations are the easiest. All other translations can be
thought of as a composition of horizontal and vertical
translations. The following examples i