If $(x_1, y_1)$ and $(x_2, y_2)$ are in direct proportion, which equation expresses this?

If $(x_1, y_1)$ and $(x_2, y_2)$ are in direct proportion, which equation expresses this?
  1. $x_1 y_2 = x_2 y_1$
  2. $x_1 x_2 = y_1 y_2$
  3. $x_1 + y_1 = x_2 + y_2$
  4. $x_1 - x_2 = y_2 - y_1$

Solution

Direct proportion: $\dfrac{x_1}{y_1} = \dfrac{x_2}{y_2}$, i.e. $x_1 y_2 = x_2 y_1$.

Asked in: IMO

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