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Question
Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
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Solution
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
\[\therefore \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|\]
\[ = \left| \frac{- \frac{3}{2} + 1}{1 + \frac{3}{2}} \right|\]
\[ = \frac{1}{5}\]
\[ \Rightarrow \theta = \tan^{- 1} \left( \frac{1}{5} \right)\]
Hence, the acute angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1 is
\[\tan^{- 1} \left( \frac{1}{5} \right)\].
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