(Q30)Show that the following points form an equilateral triangle A(a,0) , B(-a,0) , C(0,a√3).

Given A(a,0) , B(-a,0) C(0,a√3)

Distance = √((x2 - x1)2 + (y2 - y1)2)

AB = √((- - )2 + ( - )2) = √a2 = a

BC = √(( + )2 + (a√3 - )2) = √a2 = a

CA = √(( -)2+ (a √3 - )2) = √a2 = a

Now AB = BC = CA

∴ ABC is an equilateral triangle.