Show that the points (– 3, – 3), (3, 3) and (– 3√3, 3√3) are the vertices of an equilateral triangle.
Let the points be 3 (–3, –3), B (3, 3) and C (–3√3, 3√3)
Then, AB = √(3 + 3)2+( 3 + 3)2
=√(-6)2+(6)2
= √36+36
= √72
= 3√8
BC=√(-3√3+3)2+(3√3-3)2
= √(1-√3)232+(√3+1)232
= 3√[ 1+3-2√3+3+1+2√3]
= 3√8
CA = √(-3√3-3)2+(3√3-3)2
= √(-√3-1)232+(√3-1)232
= 3√[3+1+2√3+3+1-2√3]
=3√8
∵ AB = BC = CA
⇒ A, B, C are the vertices of an equilateral triangle.