Question

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

• A. ${45}^{\circ }$
• B. ${75}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

Let $A(3,-1)$ and $B(4,-2)$ be the given points and let $m$ be the slope of the line $AB$. Then,
$m=\frac{-2-(-1)}{4-3}=\frac{-2+1}{1}=-1\Rightarrow \tan \theta =-1\Rightarrow \theta ={135}^{\circ }$
So the inclination of the line with $x-$ axis is ${135}^{\circ }$

Hence, the required angle is ${45}^{\circ }.$