An engineer deploys a set of sensors. Each sensor reports its location as a point in...

 

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An engineer deploys a set of sensors. Each sensor reports its location as a point in two-dimensional space. The points are (2,7), (8,2), (6, 11), (6,5), and (11,6). Use determinants to calculate the area of the polygon formed by the sensors. Also, plot the polygon formed by the points (you'll need to do this anyway to see the proper order). The polygon that you produce should enclose the most area; no lines should cross. This will show you the proper order to use for the pair of points to use in each determinant. The area of the polygon is found by taking one half of the sum of the determinants formed by each successive pair of points. That is, if the points in counterclockwise order (clockwise will give you the negative of the area) are (x1,y1), (x2, y2), (xn, Yn), then the area is found by ... Xn X1 1 X1 X2 area = + 2 Y1 Y2 X2 X3 Y2 Y3 ++ Yn Y1 1) An engineer deploys a set of sensors. Each sensor reports its location as a point in two-dimensional space. The points are (2,7), (8,2), (6, 11), (6,5), and (11,6). Use determinants to calculate the area of the polygon formed by the sensors. Also, plot the polygon formed by the points (you'll need to do this anyway to see the proper order). The polygon that you produce should enclose the most area; no lines should cross. This will show you the proper order to use for the pair of points to use in each determinant. The area of the polygon is found by taking one half of the sum of the determinants formed by each successive pair of points. That is, if the points in counterclockwise order (clockwise will give you the negative of the area) are (x1,y1), (x2, y2), (xn, Yn), then the area is found by ... Xn X1 1 X1 X2 area = + 2 Y1 Y2 X2 X3 Y2 Y3 ++ Yn Y1 1)