(a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC = area ADEC + area CEFB - area ADFB C, ya) B(x, y2) Use this and the fact that the area of a trapezoid equals 1 -the altitude times the sum of the parallel sides to show that X1 yı 1 D E F 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, Ya) 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 (-5,-2),(4,0), (3,3). Area = i

(a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC = area ADEC + area CEFB - area ADFB C, ya) B(x, y2) Use this and the fact that the area of a trapezoid equals 1 -the altitude times the sum of the parallel sides to show that X1 yı 1 D E F 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, Ya) 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 (-5,-2),(4,0), (3,3). Area = i

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.2: Similar Polygons

Problem 11E: a Does the similarity relationship have a reflexive property for triangles and polygons in general?...

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