What type of triangle?

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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?

1. \((9,-2)\), \((4,6)\), \((20,16)\).

2. \((3, 0)\), \((-1, 0)\), \((1,21)\).

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

4. \((0, 3)\), \((0, 15)\), \((6\sqrt{3}, 9)\).

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

6. \((2, -3)\), \((-1, 1)\), \((-4, 8)\).