Question

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

Answer 1

$Given,(x_1,y_1)=(3,-1)and(x_2,y_2)=(4,-2)\text{Slope of the line}m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2+1}{4-3}$

$tan\theta =\frac{-1}{1}tan\theta =-1\Rightarrow tan\theta =-tan{45}^{\circ }(\because 1=tan{45}^{\circ })\Rightarrow tan\theta =tan({180}^{\circ }-{45}^{\circ })[\because tan({180}^{\circ }-\theta )=-tan\theta ]\Rightarrow tan\theta =tan{135}^{\circ }\Rightarrow \theta ={135}^{\circ }$