Question

The vertices of a triangle are (-2, 0), (2, 3) and (1, -3) is the triangle equilateral, isosceles or scalene?

Answer 1

Let $A(2,0),B(2,3)$ and $C(1,3)$
Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula
$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Distance between the points AB $=\sqrt{{(2+2)}^2+{(3-0)}^2}=\sqrt{16+9}=\sqrt{25}=5$

Distance between the points BC $=\sqrt{{(1-2)}^2+{(-3-3)}^2}=\sqrt{1+37}=\sqrt{37}$

Distance between the points AC $=\sqrt{{(1+2)}^2+{(-30)}^2}=\sqrt{9+9}=\sqrt{18}$

Since all the sides are of different length, the triangle is a scalene triangle.