Question

show that the points (a,a), (-a, - a)and are(-root3a, root3a) the vertices of an equilateral triangle​

Answer 1

Answer:

A = (a,a)

B = (-a,-a)

C = (-√3a,√3a)

AB=√(-a-a)²+(-a-a)²

      √4a²+4a²

        √8a²

        2√2 a

BC=√(-√3a+a)²+(√3a+a)

       √(1-√3)²a²+(√3+1)²a²

       a√[ 1+3-2√3+3+1+2√3]

       a[ √8]

       2√2a

CA = √(-√3a-a)²+(√3a-a)²

        √(-√3-1)²a²+(√3-1)²a²

        a√[3+1+2√3+3+1-2√3]

        a√8

        2√2a

∴AB = BC = CA

 it forms a eqilateral traingle

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