Question

Show that the points $( a , a )$, $( - a , - a )$ and $( - a \sqrt{3} , a \sqrt{3} )$ form an equilateral triangle.

Answer 1

A(a,a)    B(-a, -a)    C(-a√3 ,  a√3)

$AB = \sqrt{(4a^2+4a^2}=2a\sqrt2\\\\BC=a*\sqrt{(\sqrt3-1)^2+(\sqrt3+1)^2}=a*2\sqrt2\\\\CA=a*\sqrt{(\sqrt3+1)^2+(\sqrt3-1)^2}=a*2\sqrt2$

Since all sides are equal, the triangle is an equilateral Δ.