Engineering Calculus Notes 106

Engineering Calculus Notes 106 - 94 CHAPTER 1 COORDINATES...

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Unformatted text preview: 94 CHAPTER 1. COORDINATES AND VECTORS [ABCD ] is given by σ (ABCD ) A ( [ABCD ]) = 1 (x2 −x0 )(y3 −y1 )+(x1 −x3 )(y2 −y0 ) 2 where the coordinates of the vertices are A(x0 , y0 ) B (x1 , y1 ) C (x2 , y2 ) D (x3 , y3 ). Note that this is the same as 1 −− ∆ (→, →) vw 2 → − →− → −→ where − = AC and − = DA are the diagonal vectors of the v w quadrilateral. (c) What should be the (signed) area of the oriented quadrilateral [ABCD ] in Figure 1.49? B D C A Figure 1.49: Signed Area of Quadrangles (2) 13. Show that the area swept out by a line DP as P travels along a closed, simple19 polygonal path equals the signed area of the polygon: that is, suppose the vertices of a polygon in the plane, traversed in counterclockwise order, are → − = (x , y ), vi ii 19 i = 0, ..., n i.e., , the path does not cross itself: this means the path is the boundary of a polygon. ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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