Fluency exercise

## 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. $(2, -3)$, $(-1, 1)$, $(-4, 8)$.