Question

Find the slope and the inclination of the line AB if:
(i) $A=(0,-\sqrt{3})$ and $B=(3,0)$

Answer 1

Finding the slope of line AB

Let $A(0,-\sqrt{3})=(x_1,y_1)$ and $B(3,0)=(x_2,y_2)$
We know that,
Slope of line $AB=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{0-(-\sqrt{3})}{3-0}$

$=\frac{0+\sqrt{3}}{3-0}$

$=\frac{\sqrt{3}}{3}$

$=\frac{1}{\sqrt{3}}$

$\therefore$ Slope of line AB$\frac{1}{\sqrt{3}}$

Finding the inclination of line AB

Let inclination of line AB be ${\theta }^{\circ }$.

$\therefore \tan \theta =$ Slope of line AB

$\Rightarrow \tan \theta =\frac{1}{\sqrt{3}}$
$\Rightarrow \tan \theta =\tan {30}^{\circ }$ $(\because \tan {30}^{\circ }=\frac{1}{\sqrt{3}})$
$\therefore \theta ={30}^{\circ }$
Hence, the slope of a line AB is $\frac{1}{\sqrt{3}}$ and inclination is ${30}^{\circ }$.