Answer :

The three points are say A(x_{1}, y_{1}), B(x_{2}, y_{2}), C(x_{3}, y_{3})

Since they lie on a line so slope of any two points are always equal

…Equation (i)

The other set of three points are say P(3x_{1} + 2y_{1},3x_{1} – 2y_{1}), Q(3x_{2} + 2y_{2},3x_{2} – 2y_{2}), R(3x_{3} + 2y_{3},3x_{3} – 2y_{3})

Since they also lie on a line so slope between any two points is always equal

Applying Componendo and dividendo we get

Applying Invertendo we get

…Equation (ii)

Since Equation (i) & Equation (ii) are similar so the points P,Q and R lie on the line joining A,B & C

Hence Proved

Yes it is possible if we take multiples of 2 and 3

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