Math 331 Assignment

January 29, 1999

Discussion

Exercises due Monday, February 1.

Let A, B, and C be the points in the Cartesian plane that are given by

A = (0, -1) B = (3, 4) and C = (-1, 1) ,

and let T be the triangle with vertices A, B, and C.

  1. Find the point where the three medians of T meet.

  2. Find the point where the three perpendicular bissectors of the sides of T meet.

  3. Find the point where the three angle bissectors of T meet.

  4. Which of the above points are inside the triangle?

  5. How does one decide by analytic methods if a point lies inside a triangle?

  6. Find the barycentric coordinates of the point (5, 0) with respect to the vertices of the triangle T.

  7. Find the barycentric coordinates of the point (2, 2) with respect to the vertices of the triangle T.

  8. What properties of a triangle determine when any of the three canonical intersection points of the triangle, as above, does not lie inside the triangle?


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