Question

In the following examples, can the segment joining the given points form a triangle? If triangle is formed, state the type of the triangle considering sides of the triangle.

A(√2,√2 ), B(-√2, -√2 ), C( √6, √6)

Answer 1

By distance formula,

∴ d(A, B) + d(B, C) + d(A, C) … [From (iii)] 

∴ Points A, B, C are non collinear points. We can construct a triangle through 3 non collinear points. 

∴ The segment joining the given points form a triangle. 

Since, AB = BC = AC 

∴ ∆ABC is an equilateral triangle. 

∴ The segments joining the points A, B and C will form an equilateral triangle.