Equation of line in Straight lines

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Question

The tangent of angle between the lines whose intercepts on the axes are $4, - 5$ and $5, - 4$ respectively

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Solution

$Equation of the line having intercepts a, b is \frac{x}{a} + \frac{y}{b} = 1, and its slope is m = - \frac{b}{a}$
$Hence the slope of the line which makes intercepts 4, - 5 is m_{1} = - \frac{(- 5)}{4} = \frac{5}{4}, and the slope of the$
$line which makes intercepts 5, - 4 is m_{2} = - \frac{(- 4)}{5} = \frac{4}{5}$
$If θ be the acute angle between two lines having slopes m_{1} and m_{2} then \tan θ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}|$
Hence,
$\begin{matrix} \tan θ = |\frac{\frac{5}{4} - \frac{4}{5}}{1 + 1}| \\ = \frac{9}{40} \end{matrix}$
$Therefore, \tan θ = 0.23$

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

The tangent of angle between the lines whose intercepts on the axes are 4,−5 and 5,−4 respectively

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The tangent of angle between the lines whose intercepts on the axes are $4, - 5$ and $5, - 4$ respectively