Question

Show that the point (a, b + c), (b, c + a) and (c, a + b) are collinear.

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Answer 1

Answer:

The points are A(a,b+c), B(b,c+a), C(c,a+b). If the area of triangle is zero then the points are called collinear points. If three points (x1, y1), (x2, y2) and (x3, y3) are collinear then [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)] = 0. ⇒ [ a( c + a - a - b) + b( a + b - b - c) + c( b + c - c - a) ] = 0 ⇒ [ ac - ab + ab - bc + bc - ac ] = 0 = 0. ∴ the points (a,b+c), (b,c+a), (c,a+b) are collinear.