InterviewSolution
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InterviewSolution
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If the angle between two lines is `pi/4`and slope of one of the lines is `1/2`, find the slope of the other line. |
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Answer» Let `m_1` and `m_2` are the slopes of these two lines and `theta` is the angle between these two lines. Then, `tan theta = |(m_1-m_2)/(1+m_1m_2)|` Here, `theta = pi/4 and m_1 = 1/2` `:. tan(pi/4) = |(1/2-m_2)/(1+1/2m_2)|` `=> 1 = |(1/2-m_2)/(1+1/2m_2)|` `=> (1/2-m_2)/(1+1/2m_2) = 1 or (1/2-m_2)/(1+1/2m_2) = -1` `=>(1/2-m_2) = (1+1/2m_2) or (1/2-m_2) = -(1+1/2m_2)` `=>3/2m_2 = -1/2 or -1/2m_2 = -3/2` `=>m_2 = -1/3 or m_2 = 3` So, slope of other line will be `-1/3` or `3`. |
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