Math 3118, Section 3
Spring 2001
Class exercises for Thursday, February 22
- Work the exercise under heading V. on the
review sheet.
- Work the exercises under heading VI. on the
review sheet.
- Consider the triangle with vertices A = (-1,-1), B = (3,1), and C = (1,5).
- Find the following:
- P
= midpoint of the segment BC.
- Q
= midpoint of the segment AC.
- R
= midpoint of the segment AB.
- Draw a sketch showing the various points that you have found so far.
- Find the parametric representation of the line joining A and
P,
and the parametric representation of the line joining B and Q.
- Find the point where these two lines intersect. (This is similar to exercise 8.2.20 in the text.)
- Does the line joining C and R go through the point that you found in part (c)?
- Consider a triangle with "abstract" vertices A, B, and C.
- 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.)
- 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.)
- 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 ... )
- Does the line joining C and R go through the point that you found in part (c)?
- What theorem (if any) does this prove? Had you already proven that theorem when you finished problem #3?
Back to the homework assignments
Back to the class homepage