Question

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

Answer 1

The slope of the line joining the points $(3,-1)$ and $(4,-2)$ is $m=\frac{-2-(-1)}{4-3}=-2+1=-1$

Now the inclination $\left(\theta \right)$ of the line joining the points $(3,1)$ and $(4,2)$ is given by $\tan \theta =-1$

$\Rightarrow \theta =({90}^{\circ }+{45}^{\circ })={135}^{\circ }$

A slope of the line is an inclination with the x-axis.

Thus, the angle between $x$-axis and the line joining the points $(3,1)$ and $(4,2)$ is ${135}^{\circ }.$