Math 331 - February 12, 1999

Discussion

Short Test: Friday, February 19

Exercises due Wednesday, February 17

  1. Show that the barycentric coordinates of a point in the plane relative to a fixed ordered triple of non-collinear points do not depend on the choice of an affine coordinate system for the plane.

  2. Show that a 2 \times 2 orthogonal matrix must have one of the forms

    (
    cos t- sin t
    sin t cos t
    ) or (
    cos t sin t
    sin t- cos t
    ) .

  3. Let A, B, C,and D be four points in the plane. Show that the quadrilateral ABCD (obtained by tracing the line segment AB, then the line segment BC, the line segment CD, and finally the line segment DA in that order) is a parallelogram if and only if A, B, and C are non-collinear and the ordered triple of barycentric coordinates of D with respect to the ordered triple A, B, C is the ordered triple 1, -1, 1.


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