Q. 4

# Prove that if the

Answer :

The three points are say A(x1, y1), B(x2, y2), C(x3, y3)

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(3x1 + 2y1,3x1 – 2y1), Q(3x2 + 2y2,3x2 – 2y2), R(3x3 + 2y3,3x3 – 2y3)

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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