Elementary Geometry for College Students (6th Edition)

(a,a$\sqrt 3$)
The height of an equilateral triangle, which would be the y coordinate of the vertex in this case, is equal to half of the base times the square root of 3. Therefore: y=.5(2a)$\sqrt 3$ y=a$\sqrt 3$ The vertex id equidistant from the other two vertices so its x coordinate is equal to half of the base. x=.5(2a) x=a Vertex=(x,y)=(a,a$\sqrt 3$)