Question

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

Answer 1

$\text{Slope of the line segment joining the points (3, -1) and (4, -2) is}{m}_1=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{4-3}=\frac{-2+1}{4-3}=\frac{-1}{1}=-1\text{Slope of x axis is 0}If\theta \text{is the angle between x-axis and the line segment then}tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=\left|\frac{-1-0}{1+(-1)\left(0\right)}\right|=\frac{-1}{1}=-1tan\theta =-1\theta =ta{n}^{-1}(-1)\theta =\frac{3\pi }{4}\therefore \theta ={135}^{\circ }$