Question

Show that points A(a, a), B(−a, −a) and C(−a√3, a√3) are the vertices of an equilateral triangle.

Answer 1

Given points are,

A(a, a), B(–a, −a) & C(−a√3, a√3). 

Now, 

Distance between point A & B is AB.

∴ AB = √(−a − a)² + (−a − a)² 

(By distance formula) 

= √4a² + 4a² 

= 2√2a. 

Now, 

 

Hence,

AB = BC = AC = 2√2a. 

Therefore, 

Triangle ABC whose vertices are A(a, a), B(–a, −a) & C(−a√3, a√3) is an equilateral triangle. 

Hence Proved.