Math 3118, Section 1

Fall 2002

Class exercises for Monday, November 11

1. Work the exercise under heading V. on the review sheet.
    
2. Work the exercises under heading VI. on the review sheet.
    
3. Consider the triangle with vertices  A = (-1,-1),  B = (3,1),  and  C = (1,5).
   1. Find the following:
      • P = midpoint of the segment  BC.
      • Q = midpoint of the segment  AC.
      • R = midpoint of the segment  AB.
         
   2. Draw a sketch showing the various points that you have found so far.
       
   3. Find the parametric representation of the line joining  A  and  P,
      and the parametric representation of the line joining  B  and  Q.
       
   4. Find the point where these two lines intersect. (This is similar to exercise 8.2.20 in the text.)
       
   5. Does the line joining  C  and  R  go through the point that you found in part (c)?
       
4. Consider a triangle with "abstract" vertices  A, B, and C.
   1. Find the following:
      • P = midpoint of the segment  BC.
      • Q = midpoint of the segment  AC.
      • R = midpoint of the segment  AB.
      (Suggestion: You may have almost solved this already! Namely, you can make appropriate substitutions in one of your answers from exercise 2.)
       
   2. Find the parametric representation of the line joining  A  and  P,
      and the parametric representation of the line joining  B  and  Q.
      (Suggestion: In the process of building these formulas, some of your answers from part (a) will be an important input.)
       
   3. Find the point where these two lines intersect.
      (Suggestion: This is more "abstract" than the process from 3(d) above, but try to see if you can proceed analogously. Thus, you could have two expressions involving  A, B, and C  which are set equal to each other. The coefficients in those expressions probably will involve [unknown] parameter values. After any necessary simplification, try setting corresponding coefficients equal to each other ... )
       
   4. Does the line joining  C  and  R  go through the point that you found in part (c)?
       
   5. What theorem (if any) does this prove? Had you already proven that theorem when you finished problem #3?
       

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