If two vertices of an equilateral triangle have integral coordinates then the third vertex will have

Let the vertices of the equilateral triangle be (x1, y1), (x2, y2) and (x3, y3). If none of xi and yi (i = 1, 2, 3) are irrational, then area of ∆=12x1y11x2y21x3y31=retionalBut the area of an equilateral triangle=34(side)2=irrationalThus, the two statements are contradictory. Therefore, both the coordinates of the third vertex cannot be rational.