Question

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

Answer 1

We have,

$A(x_1,y_1)=(-2,3)$

$B(x_2,y_2)=(-1,0)$

$C(x_3,y_3)=(5,0)$

$D(x_4,y_4)=(2,1)$

Slope of line

$AB=\frac{y_2-y_1}{x_2-x_1}$

$m_1=\frac{0-3}{-1+2}$

$m_1=-3$

Slope of

$CD=\frac{y_4-y_3}{x_4-x_3}$

$m_2=\frac{1-0}{2-5}$

$m_2=-\frac{1}{3}$

Then,

We know that,

Angle between two slopes

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

$\tan \theta =\left|\frac{-3+\frac{1}{3}}{1+(-3)\frac{(-1)}{3}}\right|$

$\tan \theta =\left|\frac{-8}{\frac{3}{2}}\right|$

$\tan \theta =\frac{16}{3}$

$\theta ={\tan }^{-1}\frac{16}{3}$

Hence, this is the answer.