Question 752201
Q: if an equilateral triangle has 2 coordinates (-2,0),(2,0) find the third vertex?
-------------------------------------------------------------------------
A: The slope of the line segment joining (-2,0) and the third vertex is tan 60° = {{{sqrt(3)}}}. The equation of the line segment is 
{{{y - 0 = sqrt(3)(x - (-2))}}} or {{{y = sqrt(3)x + 2sqrt(3)}}}.

The slope of the line segment joining (2,0) and the third vertex is tan -60° = {{{-sqrt(3)}}}. The equation of the 2nd line segment is 
{{{y - 0 = -sqrt(3)(x - 2)}}} or {{{y = -sqrt(3)x + 2sqrt(3)}}}.

To find the third vertex, we get the point of intersection of the two line segments. By using substitution method:
{{{sqrt(3)x + 2sqrt(3)}}} = {{{ -sqrt(3)x + 2sqrt(3)}}}
{{{2sqrt(3)x }}} = 0
x = 0, substitute in the first equation
{{{y = sqrt(3)(0) + 2sqrt(3)}}} = {{{2sqrt(3)}}}
Third Vertex: (0, {{{2sqrt(3)}}})
There are two possible answers, by symmetry, the other possible answer is (0, {{{-2sqrt(3)}}})
ANSWERS: (0, {{{2sqrt(3)}}}) OR (0, {{{-2sqrt(3)}}})