Answer:
Triangle ABC is a right angled triangle.
Step-by-step explanation:
A triangle is called a right angled triangle if one of its interior angle is right angle.
The vertices of the triangle are A(0,2), B(2,-1) and C(-1,-3).
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_{AB}=\frac{-1-2}{2-0}=-\frac{3}{2}[/tex]
[tex]m_{BC}=\frac{-3+1}{-1-2}=\frac{2}{3}[/tex]
The product of slopes of two perpendicular lines is -1.
[tex]m_{AB}\times m_{BC}=-\frac{3}{2}\times \frac{2}{3}=-1[/tex]
Thus sides AB and BC are perpendicular to each other.
Since the measure of angle B is 90 degree, therefore triangle ABC is a right angled triangle.
