Question

The vertices of a triangle are $(-2,0),(2,3)$ and $(1,-3)$.

Is the triangle equilateral, isosceles or scalene?

Write answer as ${}^{\prime }{1}^{\prime }$ for equilateral, ${}^{\prime }{2}^{\prime }$ for isosceles and ${}^{\prime }{3}^{\prime }$ for 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 BC $=\sqrt{{(1-2)}^2+{(-3-3)}^2}=\sqrt{1+37}=\sqrt{37}$

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

And similarly distance between points AB = 5

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