An equilateral triangle has two vertices at the points (3, 4) and (-2, 3), find the coordinates of the third vertex.


Let the Vertices of a triangle ABC are: A(3, 4) and B (-2, 3), and C(x, y)


Length of side AB =


Length of side AB = = = units


Length of side BC = units


Length of side AC = units


(AB)2 = (BC)2


=





(AB)2 = (AC)2


=





On subtracting eqn (2) from (1), we get






…(3)


(AC)2 = (BC)2




…(4)


Solving equations (3) and (4), we get


; y =


Therefore coordinates of C are (, )


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