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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. y) sides to show that X1 yi 1 D E area ABC = X2 y2 1 2 |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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-6,-3), (6,0), (5,5). 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. y) sides to show that X1 yi 1 D E area ABC = X2 y2 1 2 |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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-6,-3), (6,0), (5,5). Area = i

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.2: The Rectangular Coordinate System And Graphing Lines
Problem 96E: Rectangle ABCD in the illustration is twice as long as it is wide, and its sides are parallel to the...
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(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x, V3) area ABC = area ADEC + area ČEFB - area ADFB 1 the altitude times the sum of the parallel B(x. ¥2) Use this and the fact that the area of a trapezoid equals A(x. y) sides to show that X1 yı 1 1 E F area ABC = 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-6,-3), (6,0), (5,5). Area = i
Transcribed Image Text:(a) In the accompanying figure, the area of the triangle ABC can be expressed as C(x, V3) area ABC = area ADEC + area ČEFB - area ADFB 1 the altitude times the sum of the parallel B(x. ¥2) Use this and the fact that the area of a trapezoid equals A(x. y) sides to show that X1 yı 1 1 E F area ABC = 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. (You should not solve (a)) (b) Use the result in (a) to find the area of the triangle with vertices (-6,-3), (6,0), (5,5). Area = i
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