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Prove that the points (a ,\ b),\ (a1,...

Prove that the points `(a ,\ b),\ (a_1,\ b_1)` and `(a-a_1,\ b-b_1)` are collinear if `a b_1=a_1b` .

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If the lines a_1x+b_1y+1=0,a_2x+b_2y+1=0 and a_3x+b_3y+1=0 are concurrent, show that the point (a_1, b_1),(a_1, b_2) and (a_3, b_3) are collinear.

If the points (a,b),(1,1)and (2,2) are collinear then

If the points (a_(1),b_(1))m(a_(2),b_(2))" and " (a_(1)-a_(2),b_(2)-b_(2)) are collinear, then prove that a_(1)/a_(2)=b_(1)/b_(2)

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