Geo2.19

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Show that the equation of the straight line passing through (x_1,y_1)\, and making an angle of \theta\, with the X-axis in positive direction is \frac{x-x_1}{\cos\theta}=\frac{y-y_1}{\sin \theta}\,.

As the straight line makes an angle 'theta' with X-axis,the slope of the line is

m=\tan\theta\, since the slope is defined by \frac{y_2-y_1}{x_2-x_1} and this also gives \frac{opp}{adj}, i.e. \tan\theta\,

Therefore the equation of the straight line is

y-y_1=\tan\theta(x-x_1)\,

that is

y-y_1=\frac{\sin\theta}{\cos\theta}(x-x_1)\,

Rearranging the variables,we get

\frac{x-x_1}{\cos\theta}=\frac{y-y_1}{\sin\theta}\,


Main Page:Geometry:Straight Lines-I

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