Scaling a Square | PuzzledQuant

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Medium

Geometry

On a table there are $4$ coins placed at the corners of a square of side $1$ , so they form a $1 \times 1$ square.

In a valid move, you choose any two coins; call them the mirror and the jumper. You then move the jumper to its mirror image with respect to the mirror. That is, imagine the mirror is the centre of a circle and the jumper lies on its circumference: you move the jumper to the diametrically opposite point of that circle.

With any number of valid moves, can you make the four coins form a square of side $2$ ?

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