Question

The points $(0,\frac{8}{3}),(1,3)$ and $(82,30)$ are vertices of

• A. an obtuse angled triangle
• B. an acute angled triangle
• C. a right angled triangle
• D. none of these

Answer 1

The correct option is D none of these

Let $A=(0,\frac{8}{3})$

$B=(1,3)$

$C=(82,30)$

Slope $AB=\frac{3-\frac{8}{3}}{1}=\frac{1}{3}$

Slope $BC=\frac{27}{81}=\frac{1}{3}$

Slope $AC=\frac{30-\frac{8}{3}}{80}=\frac{82}{3\left(80\right)}=\frac{41}{120}$

$\because$ Slope $AB=$ Slope $BC$ ..... which represents parallel lines

$\therefore$ $ABC$ is not a triangle [D]