Solution Found!
Solution: In Exercises 21–24, a, b, and c are noncollinear
Chapter 8, Problem 23E(choose chapter or problem)
In Exercises 21–24, a, b, and c are noncollinear points in R2 and p is any other point in R2. Let denote the closed triangular region determined by a, b, and c, and let be the region determined by p, b, and c. For convenience, assume that a, b, and c are arranged so that det is positive, where and are the standard homogeneous forms for the points.Let p be any point in the interior of , with barycentric coordinates (r, s, t) so that Use Exercise 19 and a fact about determinants (Chapter 3) to show that
Questions & Answers
QUESTION:
In Exercises 21–24, a, b, and c are noncollinear points in R2 and p is any other point in R2. Let denote the closed triangular region determined by a, b, and c, and let be the region determined by p, b, and c. For convenience, assume that a, b, and c are arranged so that det is positive, where and are the standard homogeneous forms for the points.Let p be any point in the interior of , with barycentric coordinates (r, s, t) so that Use Exercise 19 and a fact about determinants (Chapter 3) to show that
ANSWER:Solution 23E Barycentric coordinates are, r = = since area of = Therefore, the f