Question

Find the angle between the lines joining the points (-1, 2), (3,-5) and (-2, 3), (5,0).

Answer 1

Here,

$m_1=$ Slope of line joining (-1,2) and (3,-5)

$m_1=\frac{-5-2}{3+1}=\frac{-7}{4}$

$m_2=$ Slope of line joining (-2,3) and (5,0)

$m_2=\frac{0-3}{5+2}=\frac{-3}{7}$

Let $\theta$ be the acute angle between the given lines, then

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

$=\left|\frac{\frac{-7}{4}-\left(\frac{-3}{7}\right)}{1+\left(\frac{-7}{4}\right)\left(\frac{-3}{7}\right)}\right|$

$=\left|\frac{\frac{-37}{28}}{\frac{7}{4}}\right|$

$=\left|\frac{-37}{49}\right|$

$\tan \theta =\frac{37}{49}$

$\theta ={\tan }^{-1}\left(\frac{37}{49}\right)$

$\theta ={37.05}^o$