You and a friend decide to play the following game...

You draw three distinct dots inside a unit square.

Then your friend draws the biggest rectangle (with edges parallel to those of the square) she can which contains
**
exactly two
**
of the three dots.

With the initial three dots, you try to minimize the size of the rectangle she is able to draw.

If you play optimally, what is the area of the largest rectangle she will be able to draw containing
**
exactly two
**
of the three dots?

Give your answer to 3 decimal places.

**
Assumption:
**
The dots are allowed to share the same
$x$
or
$y$
coordinate, but not both.

The answer is 0.

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If you put the three dots "all bunched together" in the corner of the square, with the following coordinates:

Like this:

And let $\Delta \rightarrow 0$ , then you reduce the size of the rectangle she can draw to zero! ;)