2015/087) If two vertices of an equilateral triangle are $(0,0),(3,\sqrt{3})$ then find the third vertex

one point is origin $(0,0)$ and another is $(3,\sqrt3)$

the length of the side = $\sqrt{12} = 2\sqrt3$

So it is at 30 degrees with x axis.

For it to be equilateral triangle the 2^nd side shall be at 60 degrees more or 60 degrees less
that is there are 2 triangle one is at 30 degrees more that is at 90 degrees which gives co-ordinates $(0, 2\sqrt3)$
another triangle at 30 degrees less that is at -30 degrees which gives co-ordinates $(3, -\sqrt{3})$