Question

show that the three points (a,a) ,(-a,-a) and (-a root 3 ,a root 3) are the vertices of an equilateral triangle URGENT PLS REPLY

Answer 1

Step-by-step explanation:

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

may it help u ♥️