(a) In the accompanying figure, the area of the triangle ABC can be expressed as area

Chapter 2, Problem 34

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(a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC = area ADEC + area CEFB area ADFB Use this and the fact that the area of a trapezoid equals 1 2 the altitude times the sum of the parallel sides to show that area ABC = 1 2 x1 y1 1 x2 y2 1 x3 y3 1 [Note: In the derivation of this formula, the vertices are labeled such that the triangle is traced counterclockwise proceeding from (x1, y1) to (x2, y2) to (x3, y3). For a clockwise orientation, the determinant above yields the negative of the area.] (b) Use the result in (a) to find the area of the triangle with vertices (3, 3), (4, 0), (2, 1). A(x1, y1) B(x2, y2) C(x3, y3) DE F Figure Ex-34