Question

Find the angle between the $x-$axis and the line joining the points $(3,–1)$ and $(4,–2)$.

Answer 1

We know that slope of a line through the points $(x_1,y_1)\&(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}=\tan \theta$
Where, $\theta$ is the angle between the line joining the points and the positive direction of $x–$ axis .
Slope of line joining $(3,-1)\text{and}(4,-2)$ is
$m=\frac{-2-(-1)}{4-3}=\frac{-2+1}{4-3}=-1$
Now,
Slope $\left(m\right)=\tan \theta$
$\Rightarrow -1=\tan \theta$
$\Rightarrow \tan \theta =-1$
$\Rightarrow \tan \theta =\tan \left({135}^{\circ }\right)$
$\Rightarrow \theta ={135}^{\circ }$
So, Required angle $\theta ={135}^{\circ }$