For each set of points determine what sort of triangle the three coordinates form (equilateral, isosceles, right-angled and scalene). How many of each type are there in the sets of coordinates given below?

\((9,-2)\), \((4,6)\), \((20,16)\).

\((3, 0)\), \((-1, 0)\), \((1,21)\).

\((1,1)\), \((3,2)\), \((2,4)\).

\((0, 3)\), \((0, 15)\), \((6\sqrt{3}, 9)\).

\((-2,-7)\), \((1, -1)\), \((5,7)\).

\((2, -3)\), \((-1, 1)\), \((-4, 8)\).