We are given $3$ coins in a plane such that they form a equilateral triangle,say with side lenght of $2$ units. Each coin can jump over another coin so that relative to the coin being jumped on, jumping coin is same distance away after the jump relative to the stationary coin. Problem asks if it is possible to produce a bigger equilateral triangle after series of jumps.

My answer is no, because, say it is possible to make a bigger triangle, then by reverse jumping we can also get a smaller triangle . Now lets construct an $xy$ system on the leftmost vertex of the triangle, such that one coin sits on coordinates $(0,0)$, other one at ($1$,$\sqrt{3})$, and last one at $(2,0)$. Now lets consider the $x$-coordinates of the coins: $\{0;1;2\}$. Now in each jump $x$-coordinates changes. Supposing $x$-coordinates change such that we are only multiplying adding and subtracting but not dividing we cannot get fraction $x$-coordinates. But a smaller triangle would have vertices locate on a fraction, that is a contradiction?
I would appreciate comments . Thanks.