Question

Find the angle between the line joining the points (2, 0), (0, 3) and the line $x+y=1$

Answer 1

The equation between the points

$\underset{(x_1,y_1)}{(2,0)}$ and $\underset{(x_2,y_2)}{(0,3)}$

Slope of line $\frac{y_2-y_1}{x_2-x_1}$

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

Also, slope of line $x+y=1$

Converting in the form $y=mx+c$

$y=1-x$

$\Rightarrow m_2=-1$

Thus, $tan\theta =$ angle between the lines

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

$=\left|\frac{\frac{-3+2}{2}}{\frac{2+3}{2}}\right|=\left|\frac{\frac{-1}{2}}{\frac{5}{2}}\right|=\frac{1}{5}$

$\Rightarrow \theta =ta{n}^{-1}\left(\frac{1}{5}\right)$