Question

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

• A. form an acute angled triangle.
• B. lie on a straight line.
• C. form an obtuse angled triangle
• D. form a right angled triangle.

Answer 1

The correct option is B lie on a straight line.

Slope of the line joining $(0,\frac{8}{3})$ and $(1,3)$ is $m_1=\frac{3-\frac{8}{3}}{1-0}=\frac{1}{3}$
Slope of the line joining $(1,3)$ and $(82,30)$ is $m_2=\frac{30-3}{82-1}=\frac{1}{3}$
$\Rightarrow m_1=m_2$
Also, $(1,3)$ is the common point between the two lines.
$\therefore$ The given points are collinear and lie on a straight line.