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(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x3, y3) area ABC = area ADEC + area CEFB – area ADFB 1 the altitude times the sum of the parallel B(x. Y2) Use this and the fact that the area of a trapezoid equals A(x» Y1) sides to show that x1 yi 1 1 D F area ABC = X2 y2 1 |X3 _Y3 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-4,-2), (8 , 0) , (2 , 2). Area = i

(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x3, y3) area ABC = area ADEC + area CEFB – area ADFB 1 the altitude times the sum of the parallel B(x. Y2) Use this and the fact that the area of a trapezoid equals A(x» Y1) sides to show that x1 yi 1 1 D F area ABC = X2 y2 1 |X3 _Y3 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-4,-2), (8 , 0) , (2 , 2). Area = i

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
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(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x3, y3) area ABC = area ADEC + area CEFB – area ADFB B(x. Y2) 1 Use this and the fact that the area of a trapezoid equals - the altitude times the sum of the parallel A(x1, Y1) 2 sides to show that 1 X1 yi 1 D E F area ABC = X2 y2 1 |X3 _y3 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-4 , -2), (8,0), (2, 2). Area = i
Transcribed Image Text:(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x3, y3) area ABC = area ADEC + area CEFB – area ADFB B(x. Y2) 1 Use this and the fact that the area of a trapezoid equals - the altitude times the sum of the parallel A(x1, Y1) 2 sides to show that 1 X1 yi 1 D E F area ABC = X2 y2 1 |X3 _y3 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-4 , -2), (8,0), (2, 2). Area = i
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