Example 2:  Give a coordinate rule for a translation by a distance of 4 units at 30^o.

Solution:  Consider a point with coordinates (x, y) and its image with coordinates (p, q)

Draw a right triangle with the point and its image as the endpoints of the hypotenuse.  This is a 30-60-90 triangle, so the side opposite the 30^o angle is half the hypotenuse and the other side is that times the square root of 3.  Therefore we have the following picture:

From this picture we see that

 

and q = x + 2

Therefore the coordinate rule is:  (x, y) -->  

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