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
∆ (→, →)
where − = AC and − = DA are the diagonal vectors of the
(c) What should be the (signed) area of the oriented quadrilateral
[ABCD ] in Figure 1.49?
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 ),
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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