Question

Show that the points ( a, a) , ( -a , -a) , ( - root 3a , root 3a) are the vertices of an equilateral triangle.
# BRAINLIEST

Answer 1

Vertices are given A(a,a) ,B(-a,-a), C(-√3a,√3a)

AB²= {a-(-a)}² +{a-(-a)}²

Ab² =4a² +4a²

AB² = 8a²

AB =2√a


AC² = (a+√3a)² + (a-√3a)²
AC = a²+3a²+2√3a² + a² +3a² -2√3a²

Ac² = 2a²+6a²
Ac = 2√2a


BC² = (a+a)² + (a+a)²

BC ²= 4a² + 4a²

Bc² = 8a²

BC = 2√2a

so we prove that all sides are equal so it is Equilateral triangle