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 (-5,-5), (4,0), (2 , 2) . 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.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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(a)
In the accompanying figure, the area of the triangle ABC can be expressed as
Clay y3)
area ABC = area ADEC + area CEFB - area ADFB
1
- the altitude times the sum of the parallel
Bx, y2)
Use this and the fact that the area of a trapezoid equals
sides to show that
x1 yi 1
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 (-5,-5), (4,0), (2, 2).
Area =
Transcribed Image Text:(a) In the accompanying figure, the area of the triangle ABC can be expressed as Clay y3) area ABC = area ADEC + area CEFB - area ADFB 1 - the altitude times the sum of the parallel Bx, y2) Use this and the fact that the area of a trapezoid equals sides to show that x1 yi 1 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 (-5,-5), (4,0), (2, 2). Area =
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