Example 1.22.  Find parametrizations for C and -C, where C is the straight line segment beginning at and ending at .  

Solution.  Refer to Figure 1.21. The vector form of a line shows that the direction of C is .  As is a point on C, its vector equation is

  

Clearly one parametrization for    is

            

Remark.  Note that  ,  which illustrates a general principle:  If C is a curve parametrized by    for  ,  then one parametrization for    will be  ,  for  .  

Explore Solution 1.22.

Enter    and construct the line segment.

(c) 2006 John H. Mathews, Russell W. Howell