Question

prove that the points (a,b+c),(b,c+a)and (c,a+b) are collinear where  a>b>c.

Answer 1

slope(first point, second point) = (c+a-b-c)/(b-a) = (a-b)/(b-a) = -1

slope(first point, third point) = (a+b-b-c)/(c-a) = (a-c)/(c-a) = -1

slope(second point, third point) = (a+b-c-a)/(c-b) = (b-c)/(c-b) = -1

If you have 3 points forming 3 lines and the 3 lines are all parallel, then the points have to be collinear.