(1) According to the functional relationship of the straight line, we can get the coordinates of point A as (-2 √ 3,0) and point B as (0,2).

Then OA=2 √3, OB=2, in the right triangle ABO, AB = √ (OA2+OB2) = 4, ∠ Bao = 30,

According to the triangle ABC is an equilateral triangle, so ∠ cab = 60. ∠ Cao = ∠ cab+∠ Bao = 90，

Therefore, the abscissa of point C should be the same as point A,

CA = AB = BC，

∴AC=AB=4，

Then the coordinates of point C are (-2 √ 3,4).

(2) According to the meaning of the question, C and M must be on a straight line parallel to AB, and let this straight line be y= √3/3x+b,

Substituting the coordinates of point C into this straight line gives: -2+b=4, b=6,

So the analytical formula of this straight line is y= √3/3x+6,

When y= 1, √3/3m+6= 1, m=-5 √3,

Therefore, the coordinate of point M is (-5 √3, 1).