Question

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

Answer 1

Let A (2, 0), B (0, 3) be the given points.

Slope of AB = m₁
= $\frac{3-0}{0-2}$
=$\frac{-3}{2}$

Slope of the line x + y = 1 is $-$1

$\therefore m_2=-1$

Let $\theta$ be the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1

$$\begin{gathered} \therefore \tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right| \\ =\left|\frac{-{\displaystyle \frac{3}{2}}+1}{1+{\displaystyle \frac{3}{2}}}\right| \\ =\frac{1}{5} \\ \Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{5}\right) \end{gathered}$$

Hence, the acute angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1 is ${\tan }^{-1}\left(\frac{1}{5}\right)$