Problem

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

\(1\) equilateral, \(2\) scalene, \(3\) isosceles and \(2\) right-angled triangles.

If you got a different answer then think carefully about the definitions you used. Can a triangle be only one type?