If two pairs $(x_1, y_1)$ and $(x_2, y_2)$ are in inverse proportion, which equation holds?

If two pairs $(x_1, y_1)$ and $(x_2, y_2)$ are in inverse proportion, which equation holds?
  1. $x_1 y_1 = x_2 y_2$
  2. $x_1 y_2 = x_2 y_1$
  3. $x_1 + y_1 = x_2 + y_2$
  4. $x_1 - y_1 = x_2 - y_2$

Solution

Inverse: $x y = $ constant, so $x_1 y_1 = x_2 y_2$.

Asked in: IMO

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