For a 0, what kind of triangle has vertices A(a, a), B(−a, −a) and C(-√3a, √3a)?

Question

For a > 0, what kind of triangle has vertices A(a, a), B(−a, −a) and C(-√3a, √3a)?

Accepted Answer

Equilateral. AB^2 = 4a^2 + 4a^2 = 8a^2. BC^2 = (√3-1)^2a^2 + (√3+1)^2a^2 = 8a^2. AC^2 = (1+√3)^2a^2 + (1-√3)^2a^2 = 8a^2. All equal: equilateral.

For $a > 0$ , what kind of triangle has vertices A(a, a), B(−a, −a) and C $(- 3 a, 3 a)$ ?