The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin.Find the vertices of the trianlge.
Let ABC be an equilateral triangle,where BC=2a,Let A (x,0)be the third vertex of ΔABC
In equilateral trianlge ABC.AB=BC=AC ⇒AB2=BC2=AC2⇒a2=x2=(2a)2 (∵BC=2a)⇒x2=3a2 (∵BC=2a)⇒x=±√3aSo,the vertices of the triangle are (0,−1),(0,1) and (√3a,0) or (0,−a),(0,a) and (−√3a,0)