If the coordinates of two vertices of an equilateral triangle are (2, 4) and (2, 6), then the coordinates of its third vertex are

If two vertices of an equilateral triangle have the cordinates $(x_1,x_1)$ and  $(x_2,x_2)$ then the coordinates of its third vertex are 

$\left.\frac{x_1+x_2\pm \sqrt{3}\left(y_1-y_2\right)}{2},y_1+\frac{y_2\pm \sqrt{3}\left(x_1-x_2\right)}{2}\right)$

Here, we have

$x_1=2,y_1=4,x_2=2$ and $y_2=6$

Hence, the coordinates of the third vertex are 

$\left(\frac{4\pm \sqrt{3}(-2)}{2},\frac{10\pm \sqrt{3}\times 0}{2}\right)=(2\mp \sqrt{3},5)$.