The triangle formed by the points (0,-1), (-2,0), and (-1,3) is

We've been told that the triangle is formed by the three points

A = (0, -1)

B = (-2, 0)

C = (-1, 3)

To know what kind of a triangle it is, let us find the lengths of its sides by using the distance formula. We know that the distance 'd' between 2 points can be written as:

 $\mathrm{d}=\sqrt{{({\mathrm{x}}_2-{\mathrm{x}}_1)}^2 + {({\mathrm{y}}_2-{\mathrm{y}}_1)}^2}$

AB = $\sqrt{{\left(0+2\right)}^2 + {(-1-0)}^2}$

AB = $\sqrt{{\left(2\right)}^2 + {\left(1\right)}^2}$

AB = $\sqrt{5}$

BC = $\sqrt{{\left(-2+1\right)}^2 + {(0-3)}^2}$

BC = $\sqrt{{\left(-1\right)}^2+{(-3)}^2}$

BC = $\sqrt{1+9}$

BC = $\sqrt{10}$

AC = $\sqrt{{\left(0+1\right)}^2 + {\left(-1-3\right)}^2}$

AC = $\sqrt{{\left(1\right)}^2+{\left(-4\right)}^2}$

AC = $\sqrt{17}$

We can see that $\mathrm{AB} \ne \mathrm{BC}\ne \mathrm{AC}$

As all 3 sides of the triangle have different lengths, we can say that it is a SCALENE triangle.