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:

      

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