Question

PROVE THAT ALL VERTICES OF AN EQUILATERAL TRIANGLE CANNOT BE RATIONAL

Answer 1

1. Please don't use caps
2. Rational is used to describe a number, not three vertices

Answer 2

RATIONAL MEANS BOTH COORDINATES ARE RATIONAL

Answer 3

Pick some.

A: (0,0) That's Rational
B: (1,0) That's Rational
C: (1/2,???) - What's that other value? Can it be Rational?

Answer 4

Using @tkhunny 's suggestion, p = 1/2. Find q.