To avoid confusion, we will carefully distinguish between transformations of the plane and substitutions, as explained below. Substitutions A substitution , or change of coordinates , relates the coordinates of a point in one coordinate system to those of the same point in a different coordinate system . For instance, suppose the primed coordinate system is obtained from the unprimed system by moving the axes up a distance d . Then to go from the unprimed to the unprimed system one merely plugs the known values of x and y into these equations.
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