Translations

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 illustrate this.

Example 1:  Give a coordinate rule for translating a figure horizontally by 3 units.

Solution:  A horizontal translation just changes the x-coordinates of all points, so the rule is (x, y) --> (x + 3, y).  To illustrate, the blue rectangle with vertices (0, 0), (2, 0), (2, 5), and (0, 5) is translated to the red rectangle with coordinates (3, 0), (5, 0), (5, 5), and (3, 5):

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