How to find one corner of an equilateral triangle in an cartesian system

Question

How to find the coordinates of one corner of an equilateral triangle in an cartesian system if I know the coordinates of the other two corners and the $h$ (altitude)? I need the simplest solution of them all. Thank you.

Answer 1

Solve the system of the equations of the two circles centered at one point and passing through the other: $$ \begin{cases} (x-x_1)^2+(y-y_1)^2=(x_2-x_1)^2+(y_2-y_1)^2\\ (x-x_2)^2+(y-y_2)^2=(x_2-x_1)^2+(y_2-y_1)^2\\ \end{cases} $$