Geo2.16

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Show that the points $(a,b+c),(b,c+a),(c,a+b)\,$ are collinear.

The are of the triangle connected by the three points is

$\frac{1}{2}|[a(c+a-a-b)+b(a+b-b-c)+c(b+c-c-a)]|\,$

$\frac{1}{2}|[ac-ab+ab-bc+bc-ac]|\,$

$0\,$

Hence the three points are collinear.

Main Page:Geometry:Straight Lines-I

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