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 $m_{1} = - \frac{5}{4}$ , and
the slope of the line which makes intercepts $5, - 4$ is $m_{2} = - \frac{4}{5}$
If $θ$ be the acute angle between two lines having slopes $m_{1}$ and $m_{2}$ then $tanθ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}|$
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