Show that the points 0(0, 0), A(3, √3) and B(3, – √3) are the vertices of an equilateral triangle. Find the area of this triangle.


OA = √{(√3)2 + (3 – 0)2}


= √{(3) + (3)2}


= √{3 + 9}


= √{12}


AB = √{(– √3 – √3)2 + (3 – 3)2}


= √{ – 2√3)2}


= √{12}


OB = √{(3 – 0)2 + (– √3 – 0)2}


= √{9 + 3}


= √{12}


Since OA = AB = OB , ∴ equilateral triangle.


Area = 1/2 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


= 1/2[ – 3√3 – 3√3 ]


= – 3√3 sq units


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