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Prove that if the points (x1, y1),(x2, y...

Prove that if the points `(x_1, y_1),(x_2, y_2), (x_3, y_3)` are on a single line, then the points `(3 x_1+2 y_1, 3 x_1-2 y_1),(3 x_2+2 y_2, 3 x_2-2 y_2)` `(3 x_3+2 y_3, 3 x_3-2 y_3)` are also on a single line. Would this be true if we take some other numbers instead of `3` and `2` ?

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V PUBLICATION-GEOMETRY AND ALGEBRA-QUESTION BANK
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